Up until now, Mr. Bloomberg has played a relatively modest role in politics outside New York, occasionally donating to causes or candidates he favors or holding fund-raisers in his Manhattan town house to support them. But two years ago, he signaled a desire to play a bigger role in combating more extreme forces in American politics. The organization he is now establishing — and the money he will channel into races around the country — represents his most ambitious effort yet, one that will continue after he steps down in January 2014.

“This spending sends a clear message that the mayor intends to keep his wallet open after he leaves office to influence national policy around issues like guns, education and marriage equality,” said one top Bloomberg adviser, who spoke on the condition of anonymity because he was not authorized to discuss the mayor’s future. “If anything, leaving office will free him to do even more.”

Mr. Bloomberg has built a brand of politics that eschews partisanship for blunt-spoken pragmatism, often taking unpopular positions, like restricting guns and soda sizes and supporting the construction of a mosque near ground zero.

He has seemed increasingly irritated by the rhetoric of the current presidential campaign; on Wednesday he described as “gibberish” answers by President Obama and former Gov. Mitt Romney to a question about an assault weapons ban that was posed during their debate this week.

Mr. Bloomberg has tapped Howard Wolfson, a deputy mayor and a veteran of Congressional and presidential campaigns, to oversee the organization’s activities, like determining where to spend money and tailoring the themes of television advertisements. Mr. Wolfson will take a leave from City Hall to run the committee between now and Election Day.