"He did tell me what he thought were the biggest problems, in particular one problem that he thought was a big problem for the country, which I'd rather have you ask him," Mr Trump said. He declined to disclose what they were due to the private nature of their conversation but said he hopes they have a long-term relationship.
"I really liked him a lot and I'm a little bit surprised I'm telling you that I really liked him a lot."
The praise during the extraordinary interview with the paper he had described as "failing" is an example of the magnanimous attitude Mr Trump has shown since being elected in early November. He also clarified his position on some key issues in typical Trump style.
Here are the best bits you might have missed.
ON RUNNING HIS CAMPAIGN: "I got to know the country. We have a great country, we're a great, great people, and the enthusiasm was really incredible."
ON THE NEWS YORK TIMES: "I have great respect for The New York Times. Tremendous respect. It's very special. Always has been very special. I think I've been treated very rough. It's well out there that I've been treated extremely unfairly in a sense, in a true sense."
" ... The Times is, it's a great, great American jewel. A world jewel. And I hope we can all get along. We're looking for the same thing, and I hope we can all get along well."
ON RACIST ELEMENTS OF THE ALT-RIGHT: "I don't want to energise the group. I'm not looking to energise them. I don't want to energise the group, and I disavow the group."
"It's not a group I want to energise, and if they are energised I want to look into it and find out why."
"What we do want to do is we want to bring the country together, because the country is very, very divided, and that's one thing I did see, big league. It's very, very divided, and I'm going to work very hard to bring the country together."
ON THE CLINTONS: "I'm not looking to hurt them. I think they've been through a lot. They've gone through a lot."
"I think we have to get the focus of the country into looking forward."
ON CLIMATE CHANGE: "I have a very open mind. And I'm going to study a lot of the things that happened on it and we're going to look at it very carefully. But I have an open mind.
"It's a very complex subject. I'm not sure anybody is ever going to really know. I absolutely have an open mind. I will tell you this: Clean air is vitally important. Clean water, crystal clean water is vitally important. Safety is vitally important."
He also said there is "some connectivity" between human activity and climate change.
"There is something. It depends on how much. It also depends on how much it's going to cost our companies. You have to understand, our companies are non-competitive right now."
ON HIS BUSINESS AND BEING PRESIDENT: "I don't care about my company. It doesn't matter. My kids run it. They'll say I have a conflict because we just opened a beautiful hotel on Pennsylvania Avenue, so every time somebody stays at that hotel, if they stay because I'm president, I guess you could say it's a conflict of interest."
"It's a conflict of interest, but again, I'm not going to have anything to do with the hotel, and they may very well. I mean it could be that occupancy at that hotel will be because, psychologically, occupancy at that hotel will be probably a more valuable asset now than it was before, O. K.?
"The brand is certainly a hotter brand than it was before. I can't help that, but I don't care. ... The only thing that matters to me is running our country.
ON WIND: "Was I involved with the wind farms recently? Or, not that I know of. I mean, I have a problem with wind ..."
ON TECHNOLOGY: "In theory, I can be president of the United States and run my business 100 per cent, sign checks on my business, which I am phasing out of very rapidly, you know, I sign checks, I'm the old-fashioned type. I like to sign checks so I know what is going on as opposed to pressing a computer button, boom, and thousands of checks are automatically sent.
ON STEVE BANNON: "If I thought he was a racist, or alt-right, or any of the things that we can, you know, the terms we can use, I wouldn't even think about hiring him."
ON BREITBART: "It's just a newspaper, essentially. It's a newspaper. I know the guy, [Steven Bannon] he's a decent guy, he's a very smart guy. He's done a good job. He hasn't been with me that long. You know he really came in after the primaries. I had already won the primaries. And if I thought that his views were in that category, I would immediately let him go.
ON THE REPUBLICAN PARTY: "Paul Ryan right now loves me, Mitch McConnell loves me, it's amazing how winning can change things."
ON ROBOTS: When asked whether he was worried about robots replacing factory workers, Mr Trump said: "They will, and we'll make the robots too."
ON BEING PRESIDENT: "I feel comfortable. I am awed by the job, as anybody would be, but ... I feel so comfortable and you know it would be, to me, a great achievement if I could come back here in a year or two years and say - and have a lot of the folks here say, 'You've done a great job.'
ON SYRIA: "I think what's happened is a horrible, horrible thing ... I think it's a shame. And ideally we can get - do something with Syria.
ON PUTIN: "I would love to be able to get along with Russia and I think they'd like to be able to get along with us. It's in our mutual interest."
ON JARED KUSHNER: "Jared's a very smart guy. He's a very good guy. The people that know him, he's a quality person and I think he can be very helpful. I would love to be able to be the one that made peace with Israel and the Palestinians. I would love that, that would be such a great achievement. Because nobody's been able to do it."
ON WINNING: "We don't win, we can't beat anybody, we don't win anymore. At anything. We don't win on the border, we don't win with trade, we certainly don't win with the military."
ON WATERBOARDING: Trump said he asked General Mattis, who he is considering for Secretary of Defense, about waterboarding and he said 'I've never found it to be useful.'
"He said, 'I've always found, give me a pack of cigarettes and a couple of beers and I do better with that than I do with torture.' And I was very impressed by that answer."
Read the full transcript at the New York Times.
