Trump told Stahl that Clinton's phone call conceding the election was "lovely" and acknowledged that making the phone call was likely "tougher for her than it would have been for me," according to previews of the interview released by CBS.
"She couldn’t have been nicer. She just said, 'Congratulations, Donald, well done,'" Trump told Stahl. "And I said, 'I want to thank you very much. You were a great competitor.' She is very strong and very smart."
Trump's tone in the interview was in sharp contrast to his bitter attacks on the campaign trail, in which he nicknamed Clinton "Crooked Hillary" and encouraged chants of "Lock her up!" at his rallies. Among other insults, Trump also referred to his competitor as "the devil," "a bigot" and — at the tail end of the final presidential debate — "such a nasty woman."
Trump also told Stahl that former president Bill Clinton called him the following day and "couldn't have been more gracious."
"He said it was an amazing run — one of the most amazing he's ever seen," Trump said. "He was very, very, really, very nice."
During the campaign, Trump had tried to use Bill Clinton's infidelities as a way to attack and embarrass Hillary Clinton. For the second presidential debate, Trump had sought to intimidate his competitor by inviting women who had accused the former president of sexual abuse to sit in the Trump family box. Debate officials quashed the idea.
In the interview with Stahl, Trump did not rule out calling both of the Clintons for advice during his term.
"I mean, this is a very talented family," he said. "Certainly, I would certainly think about that."
Trump also reiterated on "60 Minutes" that he may keep portions of the Affordable Care Act, something he had mentioned he might do after meeting with President Obama in the White House on Thursday.
When Stahl asked whether people with preexisting conditions would still be covered after Trump repealed and replaced Obamacare, Trump said they would "because it happens to be one of the strongest assets."
"Also, with the children living with their parents for an extended period, we’re going to... very much try and keep that," Trump added, referring to portions of the healthcare act that cover children under their parents' insurance through age 26. "It adds cost, but it’s very much something we’re going to try and keep."
When Stahl questioned whether there would be a gap between the repeal of Obamacare and the implementation of a new plan that could leave millions of people uninsured, Trump interrupted her.
"Nope. We're going to do it simultaneously. It'll be just fine. It's what I do. I do a good job. You know, I mean, I know how to do this stuff," Trump said. "We're going to repeal 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. It will be repealed and replaced. I mean, you'll know. And it will be great health care for much less money."
Trump's campaign promises included fully repealing the Affordable Care Act, forcing Mexico to pay for a border wall and banning Muslims from entering the U.S.
Since winning the election, Trump and his key advisers have been backing away from some of those promises.
The "60 Minutes" interview will be broadcast on CBS at 7 p.m. Eastern time on Sunday, Nov. 13.