Soon, the campaign plans to put a transition team in place to prepare for a Trump administration, and on Thursday announced Steve Mnuchin, the head of a private investment firm, as the team’s national finance chairman.

As the presumptive nominee, Mr. Trump will begin raising money for the Republican Party and various congressional committees, his campaign said. He has largely self-funded his campaign so far — a fact he often promotes as evidence that he is not beholden to special interests — but has signaled he will raise money for his general election effort.

He also did not rule out the possibility of accepting public matching funds, saying, “I don’t know enough about it,” but he added that he would receive a briefing on the topic on Thursday.

On Tuesday, Ed Rollins, once Ronald Reagan’s campaign manager, joined Great America PAC, a “super PAC” supporting Mr. Trump, as a chairman. On a call with prospective supporters of the group on Wednesday, Mr. Rollins said its goal would not be to spend large amounts on television ads, but instead to try to plug holes for the campaign. “I think what we want to do is really examine what are the pieces that are missing,” he said.

Since last month, Mr. Trump’s congressional team has held meetings on Capitol Hill every Thursday morning when Congress is in session. It said that attendance at the meetings, which often feature a guest speaker from the Trump campaign, had swelled after the recent string of Trump victories, and that it would announce more than half a dozen endorsements in the coming weeks.

Mr. Trump’s fund-raising efforts could help court lawmakers.

“Dollars matter a lot in these tough races, so to the extent that Mr. Trump is helping us raise money, money that will help us protect our majority, he’s going to win a lot of friends in Congress,” said Representative Chris Collins of New York, one of Mr. Trump’s congressional chairmen. “That’s going to soothe a lot of folks and show he does care about the House maintaining its majority.”

The campaign has begun reaching out to Washington consultants and operatives from rival campaigns, as well as meeting quietly with Republican leaders in swing states where it believes Mr. Trump can win in November.