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There were parallel demonstrations in several other cities, and minor clashes between protesters and security forces in Alexandria, Cairo and elsewhere.

Protesters at times seemed to be re-enacting scenes from the 18-day revolt that toppled Mr. Mubarak two years ago. The loudest chants were recycled from the revolution — "Leave, leave" and "The people want the fall of the regime." Others were adapted slightly to focus on the Islamist Brotherhood, calling for an end to "the rule by the supreme guide," Mohamed Badie, the Brotherhood's spiritual leader.

It was the latest confirmation that the Islamists, who have dominated elections since Mr. Mubarak's ouster, have inherited not only his presidential palace but also the blame for Egypt's myriad problems.

On Friday, five months after President Mohamed Morsi of the Brotherhood's political party took power from Egypt's interim military rulers, the demonstrators' main complaint was that the Islamists had failed to fulfill the social welfare and social justice demands of the original revolt. A banner in the center of the square called for the repeal of the Islamist-backed Constitution, passed in a referendum last month, which opponents say failed to enshrine ironclad guarantees of individual freedoms.

"The Egyptian people had so many dreams and the reality on the ground is, everything is still the same," said Mohamed Adl, 41, a teacher who carried a sign with a handwritten poem blaming the Brotherhood for making "injustice the guard of our lives."

By early afternoon in Cairo, a few dozen protesters at one corner of the square — many of them apparently teenagers — had begun to throw rocks over a cement barrier at security forces massed around the Interior Ministry building, resuming an intermittent battle that had begun the day before in anticipation of the anniversary. The security officers, as they typically do, threw back some of the rocks, and plumes of tear gas sailed overhead past a church steeple up the street.

State media reported at around 3 p.m. that four people had been injured in the clashes with security forces near the square, in addition to 25 injured since the battle began the day before.

Osama Amir, 22, a student walking from the fight, said he did not know how it started or why. "People have lost confidence in the central security forces, so when there is a chance to beat them up, we will beat them up," he said.

A little while later, another street fight broke out when demonstrators passed the office of the Muslim Brotherhood Web site on their way to the square and threw rocks at it. Other civilians — it was unclear whether they were annoyed neighbors or Brotherhood supporters — rushed out to strike back at the protesters, and a street vendor's kiosk was burned in the melee.

Simultaneously, a group of masked men broke into the building and ransacked the Brotherhood office, overturning furniture, destroying computers and breaking glass. Neighbors of the building said the attack appeared to have been planned because the men had brought acid to break through a padlock.

The Brotherhood, hoping to avoid the kind of factional clashes that killed 10 people in December, urged its supporters to stay away from the square and observe the anniversary with community service projects around the country.

Both the Brotherhood and its opponents are now looking ahead to parliamentary elections expected to be held in April, and critics of the Brotherhood contended that its community service drive was in part an effort to curry favor with needy voters. The opposition had poured most of its energy into Friday's demonstrations, and its critics said it was once again wasting its time on street protests while the Islamists had already turned their attention to the more important electoral battle.

"It is important that people go down to the square, if for no other reason than to remind Egypt, and themselves, that something really special happened during those 18 days two years ago," said H. A. Hellyer, a researcher based here with the Brookings Institution. "That energy, however, can't stay in the square," he said. "It's got to be channeled."

But some demonstrators argued that the public protests were a first step toward building a more potent political movement that might someday counterbalance the Islamists. "Nothing tangible will come of today, and I don't think anything tangible with happen with the elections," said Ayman Roshdy, 57, a retired marketing consultant. "But there is hope. What is happening today is part of the process of building hope.

"The Islamists have been saying that they are the good guys," he continued. "Now they are in control and they are being exposed by the minute. And we are building a political movement that will help us to produce a reasonable government."

By late afternoon, other marches from around the city, some led by well-known leaders of the political opposition, were streaming toward the square and the crowd was expected to swell toward nightfall, along with the potential for more violence.