Mr. Obama’s campaign aides have also begun discussing the matter with donors in more intimate settings. In a previously scheduled meeting with about 40 top Obama donors from the New York City area on Tuesday, Jim Messina, Mr. Obama’s campaign manager, said the president and his aides had decided to help Priorities after watching Restore Our Future, a super PAC backing Mitt Romney, bludgeon Mr. Romney’s Republican rivals with millions of dollars in attack ads.

The meeting included prominent Democrats from Wall Street, the chief source of Mr. Romney’s super PAC money: Hamilton E. James, the president of the private equity firm Blackstone Group; Marc Lasry, a hedge-fund executive; Robert Wolf, the chairman of UBS Group Americas; and Ralph Schlosstein, the president of Evercore Partners…

A Democrat who advises some of the party’s top donors said many of them were “relieved and thrilled” that Mr. Obama had changed course.

“This is the strongest signal that the campaign has ever sent,” said the person, who was granted anonymity to characterize private discussions. “With the folks who are newer to political giving, the system they grew up knowing is a candidate saying, ‘No, I’m not interested in that.’ ”