Running for re-election in 2012, President Obama reluctantly endorsed fund-raising by Priorities because of fears that he would be outspent by Republicans who were more aggressive in using what was then a new vehicle for raising large amounts of money that could be used in support of a campaign but not go directly to it. But he never appeared at any of its fund-raisers.

Mrs. Clinton planned to raise money for Priorities in her campaign but initially delayed doing so because of her desire to carefully pace her campaign’s start, her pledge to make campaign finance reform a critical issue and a dispute about the super PAC’s management structure.

But supporters became anxious in recent weeks that she was squandering the enthusiasm generated by her official campaign announcement, and Mrs. Clinton decided she could no longer delay. Two leading Republican contenders have delayed officially entering the campaign, devoting their time to personally soliciting money for super PACs set up by their aides. One of them, Jeb Bush, has moved to shift costs like policy research and voter data maintenance to nonprofits that are formally independent of their campaign efforts.

The Clinton campaign and Priorities officials would not confirm the California events, but a campaign official acknowledged that Mrs. Clinton and her aides planned to do what they could to help the super PAC, within the law.

“With some Republican candidates reportedly setting up and outsourcing their entire campaign to super PACs, and the Koch brothers pledging $1 billion alone for the 2016 campaign, Democrats have to have the resources to fight back,” said one Clinton campaign official, who spoke on the condition of anonymity to explain the campaign’s thinking. “There is too much at stake for our future for Democrats to unilaterally disarm.”