Asked last month about reports he may be leaving, Mr Mattis said, "I wouldn't take it seriously at all.".
Trump said the two maintained "a very good relationship", but he allowed for the possibility Mattis would leave.
Finally, the president revealed his capacity for self-reflection and humility when Stahl asked him if there was anything he wished he hadn't said or done in his nearly two years in office. It could be that he is. "In the not-too-distant future, I think we'll know an answer". He may leave - I mean, at some point, everybody leaves. "Everybody. People leave. That's Washington".
She gave no reason for the surprise move, but observers have noted that the ascension of John Bolton as national security adviser and Mike Pompeo as secretary of state have shifted the power dynamics on Trump's national security team.
The highlight was perhaps that Trump regards Mattis, who has never publicly declared his views, a Democrat, though the president has mentioned this inkling before.More news: IMF World Bank meetings a success, say organisers
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"We're looking at a lot of different things having to do with illegal immigration", he said. "And I have other people that I'm beyond thrilled with", he said.
"I tell you what I don't want to do". Here's a passage in which Stahl asks him what he'll do if it's confirmed that the Saudi regime did in fact kill journalist Jamal Khashoggi, which seems highly likely.
"I'm not gonna get into it because we won", Trump eventually answered. We're going to get to the bottom of it and there will be severe punishment.
"I feel the same way", Trump said. She asked Trump whether he still thinks climate change was a hoax and while he said he did not think climate change was a hoax, he also told her that did not think it was man-made, or would have permanent impacts.
The U.S. leader described the retired Marine Corps general as "a good guy". Mattis also is a staunch supporter of North Atlantic Treaty Organisation, whereas Trump has questioned its value to America.