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But the rebooted campaign, known as Organizing for Action, has plunged the president and his aides into a campaign finance limbo with few clear rules, ample potential for influence-peddling, and no real precedent in national politics.

In private meetings and phone calls, Mr. Obama's aides have made clear that the new organization will rely heavily on a small number of deep-pocketed donors, not unlike the "super PACs" whose influence on political campaigns Mr. Obama once deplored.

At least half of the group's budget will come from a select group of donors who will each contribute or raise $500,000 or more, according to donors and strategists involved in the effort.

Unlike a presidential campaign, Organizing for Action has been set up as a tax-exempt "social welfare group." That means it is not bound by federal contribution limits, laws that bar White House officials from soliciting contributions, or the stringent reporting requirements for campaigns. In their place, the new group will self-regulate.

Officials said it would voluntarily disclose the names of large donors every few months and would not ask administration personnel to solicit money, though Obama aides will probably appear at some events.

The money will pay for salaries, rent and advertising, and will also be used to maintain the expensive voter database and technological infrastructure that knits together Mr. Obama's 2 million volunteers, 17 million e-mail subscribers and 22 million Twitter followers.

The goal is to harness those resources in support of Mr. Obama's second-term policy priorities, including efforts to curb gun violence and climate change and overhaul immigration procedures. Those efforts began Friday, when thousands of Obama supporters were deployed through more than 80 Congressional districts around the country to rally outside lawmakers' offices, hold vigils and bombard Congress with e-mails and phone calls urging members to support stricter background checks for gun buyers.

"There are wins we can have on guns and immigration," Jon Carson, the group's new executive director, told prospective donors on a conference call on Wednesday, according to people who participated. "We have to change the conventional wisdom on those issues."

But those contributions will also translate into access, according to donors courted by the president's aides. Next month, Organizing for Action will hold a "founders summit" at a hotel near the White House, where donors paying $50,000 each will mingle with Mr. Obama's former campaign manager, Jim Messina, and Mr. Carson, who previously led the White House Office of Public Engagement.

Giving or raising $500,000 or more puts donors on a national advisory board for Mr. Obama's group and the privilege of attending quarterly meetings with the president, along with other meetings at the White House. Moreover, the new cash demands on Mr. Obama's top donors and bundlers come as many of them are angling for appointments to administration jobs or ambassadorships.

"It just smells," said Bob Edgar, the president of Common Cause, which advocates tighter regulation of campaign money. "The president is setting a very bad model setting up this organization."

Mr. Obama's new organization has drawn rebukes in recent days from watchdog groups, which view it as another step away from the tighter campaign regulation Mr. Obama once championed. Over the past two years, he has reversed course on several campaign finance issues, by blessing a super PAC created by former aides and accepting large corporate contributions for his second inauguration.

Many traditional advocacy organizations, including the Sierra Club and the National Rifle Association, are set up as social welfare groups, or 501(c)(4)'s in tax parlance. But unlike those groups, Organizing for Action appears to be an extension of the administration, stocked with alumni of Mr. Obama's White House and campaign teams and devoted solely to the president's second-term agenda.

Robert K. Kelner, a Republican election lawyer who works with other outside groups, said the arrangement "presents a rather simple loophole in the otherwise incredibly complex web of government ethics regulations that are intended to insulate government officials from outside influence."

The closest precedents for Organizing for Action exist at the state level. In New Jersey, a 501(c)(4) called the Committee for Our Children's Future, set up by friends of Gov. Chris Christie, has run hundreds of thousands of dollars' worth of advertising praising Mr. Christie's proposals.

In New York, Gov. Andrew M. Cuomo encouraged the formation of a nonprofit group, the Committee to Save New York, that is run by business leaders allied with him, and it has raised millions of dollars from corporations, private sector unions, and individuals. The group supported Mr. Cuomo's agenda — but it also thrust him into controversy when The New York Times revealed that gambling interests poured $2 million into the group as Mr. Cuomo was developing a proposal to expand casino gambling.

Organizing for Action said it would accept unlimited personal and corporate contributions, but no money from political action committees, lobbyists or foreign citizens. Officials said they would focus — for now — on grass-roots organizing, amplified by Internet advertising. Friday's "day of action" involved half a million dollars' worth of targeted Internet ads and events in Florida, Maine, Pennsylvania and California, among other states.

"O.F.A.'s first day of action was about bringing the issue of closing background-check loopholes into communities across the country that feel very strongly about supporting the president's plan to reduce gun violence," said Katie Hogan, a spokeswoman for the group.

Organizing for Action has also promised to steer clear of electoral politics, unlike the politically active nonprofit groups like the right-leaning Crossroads Grassroots Policy Strategies and Americans for Prosperity. Such groups spent hundreds of millions of dollars on advertising during the recent election campaign season, ostensibly for issue advocacy, spurring a wave of lawsuits, ethics complaints from campaign watchdogs and criticism from Mr. Obama himself.

But the distinction between campaigning and issue advocacy may be hard for Organizing for Action to maintain in the prelude to the 2014 elections, especially if it continues its emphasis on pressing lawmakers on delicate issues like immigration and guns.

In Wednesday's conference call, Mr. Carson said the group hoped to form partnerships with other 501(c)(4) groups on the left, including America Votes, which was at the center of Democratic efforts to defeat President George W. Bush in 2004 and now serves as a coordinator for progressive advocacy organizations. He also said Organizing for Action wanted to be a counterweight to grass-roots organizations on the right, like the N.R.A., according to people who took part in the call.

There should be "as much of a price to pay if you tick off the gun violence people" as there is for angering the N.R.A., Mr. Carson said, according to those people. "Let's build an organization that means that Republicans are embarrassed to have climate change deniers running for office."