The campaign-style effort to push gun-control legislation was the work of an offshoot of Obama for America, the president’s 2012 reelection organization, that is now trying to maintain political momentum for the president’s policy priorities.

The new group, Organizing for Action, has the president’s full backing, some of the same key political staff — even the same acronym. But it has a different mission and is playing under a looser set of rules that allow it to accept unlimited campaign contributions and cloak much of its activities in secrecy.

The first organization of its kind so closely aligned with the political brain trust of a sitting president, Organizing for Action has generated strong criticism from watchdog groups who say it could permit undue influence from wealthy contributors.

In addition to gun control, the new group’s priorities include pushing on immigration reform and combatting climate change — issues organizers refer to as “the people’s agenda.”

Jim Messina, Obama’s campaign manager turned national chairman of Organizing for Action, kicked off the group’s “founders summit” this week at a swanky hotel a couple of blocks from the White House.

“If Americans don’t organize in support of the issues they believe in and if we don’t help them do it, then lobbyists and special interests will drive Washington just like they did for decades,” Messina told a group of about 60 Obama volunteers, donors, and former campaign staff.

The group invited media to witness a small portion of each day in an effort to diffuse the controversy that flared up around its formation, including skepticism about its claims to be nonpartisan and concern that it will unfairly influence the 2014 mid-term elections.

David Plouffe, Obama’s former senior adviser, said Organizing for Action formed because people saw over the past four years how difficult it has been for Obama to move his agenda in the face of a recalcitrant Congress.

“Not many of us are naive anymore,” Plouffe said. “This is something that should be celebrated, not criticized.”

But raising unlimited money and using it to pressure Congress represents an unprecedented thrust by a White House-backed group into America’s rapidly evolving, loosely regulated campaign environment.

Some liberal Democrats are skeptical of the new organization’s power to move Republicans in Congress, and worry that it will instead be used to pressure Democrats into a more centrist position on the nation’s debt crisis. Others worry it will siphon contributions away from other Democratic groups advocating on behalf of labor, minorities, and women.

Washington observers also wonder if the tax-exempt “social welfare” organization will gradually morph into the Democratic version of the politically active Crossroads Grassroots Policy Strategies, founded by Karl Rove, the former top political adviser to President George W. Bush. Crossroads GPS and its super PAC, American Crossroads, spent heavily to influence the outcome of the 2012 elections and the 2010 midterms, when Republicans took over the House of Representatives.

Obama himself, citing suspicion and puzzlement around the organization, tried to allay concerns at an Organizing for Action dinner this week. The group is not just a “mechanism to try to win the next election in 2014,” Obama said. “No, I actually just want to govern — at least for a couple of years.”

Critics are not soothed.

Fred Wertheimer, president of Democracy 21, which advocates for greater transparency in campaign finances, wrote to Obama, asking him to dismantle Organizing for Action. Wertheimer argues that the nonprofit group raises serious conflict of interest questions.

“OFA is an unprecedented entity linked directly to the president and raising large contributions, creating the potential opportunity for buying corrupting influence over administration policies,” Wertheimer said in an interview. “This is the transformed organization that ran his campaign. It’s an arm of his presidency.”

In response to criticism, Organizing for Action recently said it would no longer accept donations from corporations — nor will it take money from lobbyists, political action committees, of foreign governments.