Donald Trump will appear in his first extensive post-election interview Sunday on “60 Minutes” at 7 p.m. ET

After running a heated campaign predicated in part on rolling back President Obama’s signature healthcare law, Donald Trump is now signaling an openness to keeping the Affordable Care Act in some form.

People with pre-existing conditions will still be covered in the version of health care that Trump wants to see replace Obamacare, he said in a wide-ranging interview with CBS News’ Lesley Stahl on “60 Minutes.”

“It happens to be one of the strongest assets,” Trump said about insuring people with pre-existing conditions. “It adds cost, but it’s very much something we’re gonna try and keep.”

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And, he told Stahl, that there will be no lapse between the repeal of Mr. Obama’s signature health-care law and its replacement by his version. The’re won’t be “a two day period” or “a two year period where there’s nothing. It will be repealed and replaced. I mean, you’ll know. And it’ll be great health care for much less money,” he promised.

“Either Obamacare will be amended, or repealed and replaced,” Mr. Trump told the Wall Street Journal in an interview published Friday.

Mr. Trump favors keeping in place protections for patients with pre-existing conditions, along with a measure that allows parents to keep their children on their insurance policies until the age of 26, the Journal said, and it also reported that during their meeting Thursday, Mr. Obama asked the president-elect to reconsider repealing it.

In fact, Mr. Trump told the Journal that a big reason for his shift from his call for a full repeal was his meeting with Mr. Obama, who, he said, suggested areas of Obamacare to keep intact. “I told him I will look at his suggestions, and out of respect, I will do that,” Mr. Trump said.

The measures on pre-existing conditions and keeping children on their parents’ policies are popular even among the most partisan Republican legislators who have called for a full repeal of the law, and they have been included in proposals that would replace the ACA with a GOP-backed alternative. House Speaker Paul Ryan’s “Better Way” healthcare plan, for example, would also prevent insurance companies form denying coverage to those with existing conditions and would keep the parental provision.

Trump himself has said before in a Republican primary debate that he would want to keep some measures Obamacare instituted.

“I would absolutely get rid of Obamacare. I want to keep pre-existing conditions. It’s a modern age, and I think we have to have it,” Mr. Trump said in February at the CNN-Telemundo debate in Texas. “I would absolutely get rid of Obamacare. I want to keep pre- existing conditions. It’s a modern age, and I think we have to have it.”

But Trump’s recent answer in the Journal is a softening even from the plan his campaign team recently put on his website for his first 100 days in office, which explicitly calls for a piece of legislation called the “Repeal and Replace Obamacare Act.” The legislation, according to Mr. Trump’s plan, “fully repeals Obamacare and replaces it.”

In the interview with “60 Minutes,” the president-elect also said talked about the call he received from Hillary Clinton when she conceded.

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

And former President Bill Clinton called Thurday, Mr. Trump said.

“He couldn’t have been more gracious,” the president-elect said. “He said it was an amazing run. One of the most amazing he’s ever seen.”