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French flags flew in the center of the city and a crowd reported to be in the thousands chanted, "Thank you, France" and "Long live François Hollande" as Mr. Hollande swept into town, accompanied by his ministers of defense, foreign affairs and development and flanked by the Malian president, Dioncounda Traoré.

But French officials and analysts fear that jubilation may shortly give way to increased ethnic tensions and violence — and it remains unclear if French or African forces will be sent to root out the Islamist fighters that have fled from Timbuktu and other northern cities, or when such operations might take place.

"It's going to take a few more weeks," Mr. Hollande said, according to news media reports, but he insisted that security responsibilities would soon be handed off to Malian and African forces. "It is not our role to stay," he said. "Our African friends will be able to do the work that was ours until now."

France has a force of about 3,500 in the country, and about 3,000 soldiers from several African nations have flowed in since the French intervened last month. European military officers are to begin training the divided and disorganized Malian Army in the coming weeks or months, too, but it is unlikely that the African or Malian forces will be prepared to conduct operations against the militants before the rainy season, which generally lasts through August or so, meaning an offensive into the countryside might have to wait until then.

In the meantime, human rights groups have reported a number of abuses committed by Malian soldiers since the French military intervention began in mid-January, including accusations that soldiers conducted summary executions of civilians suspected of militant ties.

Since the liberation of Timbuktu and the northeastern city of Gao, there have also been widespread reports of looting and attacks against Arab and Tuareg residents, with black residents accusing them of collaboration with Islamist fighters; some of the groups under attack have reportedly fled.

Pressing, too, is the political question of the Tuaregs, some of whom have long called for an independent state in upper Mali. Their uprising last year set the stage for the militant Islamists who initially joined with the Tuaregs and overran the north.

French officials are pressing Mr. Traoré, the Malian president, to start negotiations quickly with Tuareg rebels, most of whom have now disavowed the Islamists. The majority of Tuaregs, the French believe, will agree to remain in a sovereign Mali with more guarantees of political autonomy, and the French hope that a deal will lead to early national elections; Mr. Traoré this week announced elections for the summer.

The French Foreign Ministry has called on the Malian government to open talks with "legitimate representatives" and "non-terrorist-armed groups" in the north, especially the secular Tuareg National Movement for the Liberation of Azawad, known as the M.N.L.A.

Mr. Traoré has said he is open to talks with the M.N.L.A., but only so long as it forgoes its demands for independence. French officials have pressed the group to do so.

"Mali must enter a phase of national reconciliation," said Jean-Yves Le Drian, the French defense minister, in an interview on France Inter radio last week. The groups involved in that process "must pronounce themselves against terrorism, very clearly, and against any desire for a splitting of Mali's territory," he said. "This country needs to return to democratic legitimacy. This is not yet the case." Paris would also like the presence of up to 5,000 United Nations peacekeeping troops, officials say, to further underline the international support for an integral Mali and further dilute the French presence.

Military considerations remain, though. In Washington, military and counterterrorism officials have applauded the speed and efficiency of the French-led operation, but they have also suggested that the militants may have ceded the northern cities with little resistance in order to prepare for a longer, bloodier counterinsurgency.

"Longer term, and the French know this, it's going to take a while to root out all these cells and operatives," Michael Sheehan, the Pentagon's top special operations policy official, told a defense industry symposium on Wednesday.

The Islamist fighters in Mali number between 2,000 and 3,000, officials and analysts estimate. It remains unclear how many have been killed in French airstrikes and ground operations, but a great number remain, likely occupying a network of caves and underground redoubts constructed in the mountains in the far north, near the Algerian border, analysts and officials say.

Prime Minister Mariano Rajoy made a televised address at a meeting of his party's national executive committee in Madrid.

Sheik Ahmad Moaz al-Khatib, leader of the Syrian opposition council, at the conference.

Moscow has been encouraged by Sheik Khatib's suggestion, which he repeated here, that he might be willing to talk to representatives of the Syrian government under certain conditions. But European and American officials expect that offer to go nowhere now that the Sheik's own colleagues in the opposition have attacked it.

The series of side meetings here at the annual Munich Security Conference seemed to confirm the fissures over what to do about Syria, including a new disagreement between the United States and some of its European allies over whether to provide the rebel fighters with more powerful weapons.

Senior European officials here said that Britain and France were both urging the Obama administration to stop blocking allies in the Gulf, like Qatar, from providing the rebels with more sophisticated arms and intelligence assistance.

The officials argue that the current Syrian stalemate means that the opposition is not winning, and Mr. Assad is not losing. An opposition with better military means could break the confidence of Mr. Assad and his allies and push him to negotiate with the opposition, the officials argue.

But President Obama, American officials here said, remained unconvinced about the positive effects of further militarizing the conflict, pointing to his recent interview with The New Republic, in which he asked, "In a situation like Syria, I have to ask, can we make a difference in that situation?" American officials fear the advanced weapons would fall into the hands of Islamists with an international agenda who have joined the fight in Syria alongside rebels focused on overthrowing Mr. Assad.

The conference, in its 49th year, is considered the premier trans-Atlantic conference for security officials and analysts.

Vice President Joseph R. Biden Jr., representing an Obama administration in transition to another term, carefully made no news in a well-received speech designed to reassure European allies of a continuing focus on European concerns despite the American "pivot to Asia."

And while Mr. Biden implicitly criticized Russia for supporting the government of President Bashar al-Assad, he gave the Syrian opposition little hope that Washington would change its mind about allowing more sophisticated arms to flow to the rebels.

Mr. Biden repeated America's demand that Mr. Assad relinquish power, which was immediately criticized the Russian foreign minister, Sergey V. Lavrov, as "the single biggest reason for the continuation of the tragedy in Syria." And while Mr. Biden listed the $365 million in humanitarian aid to Syrian refugees and $50 million in nonlethal assistance to the Syrian opposition provided by the United States, he promised nothing that would help turn the war in their favor.

"As the Syrian people have their chance to forge their own future, they will continue to find a partner in the United States of America," Mr. Biden said.

Mr. Biden also spoke about Iran, repeating that the United States was willing to open direct, bilateral talks with Tehran over its nuclear program, but he insisted that Iran must show it is serious and that the talks would be substantive. "We're not prepared to do it just for the exercise," Mr. Biden said.

The Obama administration has been pushing for months to hold direct talks with Tehran, calculating that there is a window for diplomacy before Iran's elections in June. But in recent weeks, Iranian officials have thrown cold water on the idea. Indeed, Tehran has balked at setting a date or location for multilateral talks with the United States and other major powers.

In a sign of the intransigence of the conflicts over Syria's future, the United Nations negotiator for the country, Lakhdar Brahimi, expressed pessimism Friday during a panel discussion at the security conference. "I am much more conscious of the difficulties, of the country being broken down day after day, than I am of a solution," said Mr. Brahimi, who also met with Sheik Khatib.

Sheik Khatib — who directs a Syrian opposition council cobbled together with Washington's help, and pressure, to try to unify a fractured movement — found himself struggling last week to tamp down criticism of his suggestion that he would be open to talking with representatives of the Assad government. (His terms of participating were that 160,000 prisoners had to be released and that Syrians abroad could renew their passports.)

But his own colleagues strongly objected, saying that the talks must focus on the removal of Mr. Assad. While Sheik Khatib reiterated his offer here, saying that "as a gesture of good will, we are ready to sit at the negotiating table with the regime but we don't want their hands to be full of blood," he refused to provide any details, instead issuing a long indictment of the Assad government.

One senior European official said that even if Sheik Khatib were serious about talks with the regime, his colleagues would most likely force him to backtrack.

Sheik Khatib also called for the West to destroy the Syrian government's air power, which would require the direct military intervention Washington has ruled out.

Mr. Lavrov, for his part, expressed the standard Russian position: no international military involvement, no solution by military means, an immediate cease-fire and negotiations among all parties, including Mr. Assad. He said that the biggest threat in Syria was "the possibility that the rebels get hold of the chemical weapons" currently under Mr. Assad's control.

Mr. Biden did not speak to reporters after his bilateral meetings, and there were no briefings for the news media.

Russia, Syria's main arms supplier, has blocked three United Nations Security Council resolutions on the Syrian conflict, which has killed more than 60,000 people in nearly two years.

With his death on Friday at 88, it seemed only fitting to ask that question once more — in retrospect.

There is no doubt that Mr. Koch restored the spirit of the city after years of urban decay that had crystallized in the city's near bankruptcy, and that reached a nadir of sorts in 1977 with the Son of Sam killings, a blackout and riots. Mr. Koch, a Democrat, took office in January 1978 and, with his moxie, was able to quickly create a sense among New Yorkers that someone was fighting to turn the city around.

"The city needed hope, it needed a champion, it needed a voice," said Mitchell Moss, a professor of urban policy at New York University. "Ed Koch became that voice."

Even the Rev. Calvin O. Butts III, the pastor of Abyssinian Baptist Church in Harlem, who tangled frequently with Mr. Koch over what he felt was the mayor's insensitivity to African-Americans, said Mr. Koch was the right mayor for his time.

"If you've got to have a mayor for New York City, you need a guy like Ed Koch because he's a rough-and-tumble kind of guy who speaks up and fights back," he said.

The Koch-era legacy is substantial. Experts cite the investment of billions of dollars in rebuilding abandoned housing, which revived desolate areas of the South Bronx, Harlem and central Brooklyn; the restoration of the city's fiscal integrity to the point where banks and government watchdogs were ready to let it manage its own finances; the rehabilitation of neglected parks; the genesis of Times Square's transformation from a sleazy, dangerous crossroads to a family-friendly entertainment and office center; the trading in of federal money designated to build a new West Side Highway for money that would buy subway trains and buses; the pressure on the Metropolitan Transportation Authority to virtually eliminate subway graffiti; and the enacting of a campaign finance law in 1988 under which candidates would limit their spending in exchange for receiving public matching funds.

On the ledger's deficit side, experts say Mr. Koch needlessly antagonized African-American New Yorkers and allowed his reputation for let-the-chips-fall-where-they-may integrity to be tarnished by corruption scandals that started in the Parking Violations Bureau and raised questions about his alliances with political bosses. Together, those failures might have cost him a fourth term.

Fred Conrad/The New York Times

On Election Day, Nov. 3, 1981, Mayor Edward I. Koch was swarmed by reporters after voting in Greenwich Village. Mr. Koch, who died on Friday, has been credited with helping revive desolate areas in the South Bronx and elsewhere, restoring the city's fiscal integrity and rehabilitating its neglected parks.

While opinions about the former mayor may vary, there is no doubt he left a notable mark in several areas.

HOUSING

To grasp the scope of Mr. Koch's accomplishment, consider the visit that President Jimmy Carter made in 1977 to the South Bronx, where he stood with Mayor Abraham D. Beame in a rubble-strewed patch of Charlotte Street against a backdrop of ghostly, gutted buildings. That characteristic landscape changed dramatically starting in 1986 with a 10-year plan by Mr. Koch that led to the spending of more than $5 billion on building low- and moderate-income housing and on rehabilitating vacant buildings. The program eventually created more than 150,000 affordable apartments, according to Ted Houghton, executive director of the Supportive Housing Network of New York. Charlotte Street itself was turned into a row of suburban-style ranch houses that a few years ago were selling for $500,000 apiece. There are few lots in the Bronx that sit empty anymore.

"When you walk through today's vibrant neighborhoods in Harlem, Bed-Stuy and the South Bronx, thank Ed Koch," Mr. Houghton said in an e-mail. "If it wasn't for his 10-year housing plan, we'd still be looking at acres and acres of abandoned buildings, like one continues to see in a lot of less fortunate, older Eastern cities."

PARKS

In the years before Mr. Koch became mayor, many of the city's signature parks had gone to seed — partly as a result of lack of money, but also because of a poorly administered and patronage-ridden bureaucracy. Central Park had become so dangerous it was ridiculed by late-night comedians.

Marcus Yam for The New York Times

Holly Leicht, executive director of New Yorkers for Parks.

"In the Koch administration, the parks took on an elevated position that they hadn't really had since the Robert Mosesera," said Holly Leicht, executive director of New Yorkers for Parks.

Parks commissioners like Gordon J. Davis and Henry J. Sternde centralized their department, delegating more authority to officials in the boroughs and appointing new parks administrators for Central Park and Prospect Park. Those administrators ultimately cobbled together public-private partnerships that have rejuvenated both parks. The Sheep Meadow, virtually a dust bowl when Koch took office, was turned into a green carpet, and the crumbling Bethesda Fountain into an aesthetic jewel. Adrian Benepe, who was a park ranger when Mr. Koch took office and eventually became the commissioner under Mayor Michael R. Bloomberg, said a key moment was "having Simon and Garfunkel do a concert in Central Park in the early '80s, because it showed that Central Park was safe and fun at night."

CRIME

Mr. Koch's record on crime is more mixed. A few years into his tenure, crime began to recede, with murders declining to 1,386 in 1985 from 1,818 in 1980. Jeremy Travis, president of John Jay College of Criminal Justice, who was a special adviser to Mr. Koch during his third term, said gains were made by techniques like concentrating police personnel on open-air drug markets where people were brazenly lining up to buy drugs. But the unseen rise of the crack cocaine epidemic in the mid-1980s led to a resurgence, as easy profits enticed many amateurs into drug dealing and neighborhood wars broke out. The administration's response was "heroic," Mr. Travis said, but hobbled by understaffing in the Police Department — about 26,000 officers at the time — as a result of the layoffs demanded by the 1970s fiscal crisis.

Marcus Yam for The New York Times

Jeremy Travis, president of John Jay College of Criminal Justice.

"If you dialed 911, you couldn't get a car to the scene in time," Mr. Travis said. "An under-resourced department is not effective in fighting crime."

By 1990, the year after Mr. Koch left office, murders hit a historic peak of 2,251. The situation did not begin to be reversed until the city hired 5,000 more officers late in the administration of Mayor David N. Dinkins. Another form of crime, corruption, was spawned in Mr. Koch's Parking Violations Bureau. There were no revelations suggesting that Mr. Koch personally profited, but the scandals left a stain because they indicated he was sometimes willing to make patronage appointments to sustain the backing of Democratic bosses like Meade H. Esposito, Donald R. Manes and Stanley M. Friedman.

HEALTH

Larry Kramer, the gay rights advocate who wrote the play "The Normal Heart"about the AIDS epidemic, recently accused Mr. Koch of ignoring the disease's spread in a city with a large gay population because "he was terrified everyone would find out he was gay and he would lose his support from the real estate industry." Mr. Kramer said Mr. Koch did not "tell people to change their behavior" and refused to meet with or finance gay activists. (Though he once responded to a questioner that he was heterosexual, Mr. Koch repeatedly said that his love life was nobody's business but his own.)

Todd Heisler/The New York Times

Larry Kramer, a gay rights advocate.

Stanley Brezenoff, the chief executive officer of Continuum Health Partners and a former deputy mayor under Mr. Koch, offered a different picture of Mr. Koch's response to the AIDS epidemic. "It took a long time to recognize what was going on," Mr. Brezenoff said, "and as we came to grips with it we became more focused on identifying concrete steps to take." Mr. Koch, he said, agonized over a step like closing bathhouses used for promiscuous sex because it meant having to dispatch "investigators into bathhouses and spying on people in their most private moments."

One health policy decision Mr. Koch came to regret was the closing — for reasons of poor performance — of Sydenham Hospital in Harlem. Mr. Koch said in recent years that he had not fully appreciated how important the hospital was to black doctors, who often had trouble receiving admitting privileges elsewhere.

Mr. Brezenoff, who was president of the city's Health and Hospitals Corporation from 1981 to 1982, credited Mr. Koch for spurring "the renaissance" of the agency, which had been in disarray, and for focusing its mission on primary care.

RACE RELATIONS

From the beginning, Mr. Koch frequently found himself at loggerheads with black ministers and politicians. The Sydenham closing stirred enormous resentment in Harlem. So did Mr. Koch's abrasive style, which led him to call antipoverty organizers who were abusing the system "poverty pimps." He might also have realized that more than a few of his white supporters appreciated such tough talk.

Marcus Yam for The New York Times

The Rev. Calvin O. Butts III, pastor of Abyssinian Baptist Church in Harlem.

"He was a politician and he knew what crowd he had to play to," Mr. Butts, pastor of Abyssinian Baptist Church in Harlem, said.

But David R. Jones, president of the Community Service Society of New York and a former Koch adviser, pointed out that Mr. Koch assembled the most diverse team of deputies and commissioners City Hall had ever seen, includingBasil A. Paterson,Herman Badillo and Mr. Jones. Later, he appointed Benjamin Ward as the city's first black police commissioner.

Mr. Koch also suffered because of racially charged episodes that sprang up on his watch: the 1984 shooting death of a 66-year-old black woman, Eleanor Bumpurs, by a white police officer during an eviction; the 1986 beating of three black men by a white gang in Howard Beach, Queens; the shooting death of Yusuf K. Hawkins by white youths weeks before the 1989 election.

Despite his condemnation of the mob beatings, it was hard to tamp down a sense among blacks that his public rhetoric — in the 1988 presidential campaign, for example, he said Jews would be "crazy" to vote for Jesse Jacksonbecause of his "Hymietown" slur about New York and his support for a Palestinian homeland — may have helped foster an atmosphere in which some young whites felt emboldened to commit such assaults.

Still, Mr. Koch seemed to redeem himself in his post-mayoralty. The Rev.Al SharptonJr. became a friend, and Mr. Butts, who once said Mr. Koch was "worse than a racist, he was an opportunist," said last week: "I never got the impression that he was a racist. He had his prejudices like everybody else and he allowed his temper and his I-know-what's-best-for-everybody attitude to get in the way of sound judgment."

TRANSIT

With its graffiti-coated subway cars and frequent breakdowns, the transit system Mr. Koch inherited had become one of the bleakest symbols of the city's tailspin. Ridership had fallen to its lowest level since 1917, even before the modern subway system had been completed, according to Gene Russianoff, staff attorney for the Straphangers Campaign.

While he had few direct powers to change matters, Mr. Koch harangued the Transportation Authority for its crackling, inaudible announcements; doubled, to $200 million, the city's contribution for rebuilding; and urged that dogs patrol the subway yards, an idea that was barely tried. While originally a proponent of the West Side Highway, Mr. Koch eventually fought for trading in the federal highway funds for $1 billion to buy new subway cars. The last graffiti-marked car was taken out of service in his last year in office.