“It was a lovely call, and it was a tough call for her — I mean, I can imagine, tougher for her than it would have been for me,” Mr. Trump said. “She couldn’t have been nicer. She just said, ‘Congratulations, Donald, well done.’”

Mr. Trump, who on Thursday said he would seek Mr. Obama’s counsel about the presidency, said he would consider asking for Mr. Clinton’s as well.

Mr. Trump also promised that there would be no lapse in health insurance for millions of Americans covered under the Affordable Care Act when he repeals and replaces the law.

“We’re going to do it simultaneously — it’ll be just fine,” Mr. Trump said. “That’s what I do. I do a good job. You know, I mean, I know how to do this stuff. We’re going to repeal it and replace it. And we’re not going to have, like, a two-day period and we’re not going to have a two-year period where there’s nothing.”

And speaking of olive branches — Mitt Romney

Mr. Trump has quietly reached out to Mitt Romney, the 2012 Republican nominee who took an impassioned stand against Mr. Trump during the campaign.

The call came after Mr. Trump’s surprise victory on Tuesday night, according to two people briefed on it, although it was unclear how it went and what was said.

Aides to Mr. Trump and Mr. Romney did not respond to requests for comment.

Gloria Allred eyes the Paula Jones model.

With her eye on the right’s Paula Jones legal crusade of the 1990s, Gloria Allred, the civil rights lawyer representing women who have accused Mr. Trump of sexual assault, is trying to lure the president-elect into a legal battle before he takes office.