Last week the New York Times reported that Mr Tillerson was astonished at how little Mr Trump grasps the basics of foreign policy.
"I have never considered leaving this post", Tillerson said October 4, dismissing the reports as "erroneous" and "petty nonsense". It followed a weekend where Trump appeared to undercut Tillerson's approach to diplomacy with North Korea over its intensifying nuclear weapons program.
"No, I didn't undercut anybody". He also said he still has confidence in Tillerson as secretary of state. Tillerson has publicly complained about the slow pace of getting his assistant secretaries and other deputies nominated and confirmed. "I don't believe in undercutting people", Trump said.
"I think it's fake news, but if he did that, I guess we'll have to compare IQ tests". Regardless of who would win that competition - Trump implied he win - it would do nothing to answer the question of who is smarter.
State Department officials did not immediately respond to requests for comment.
If you've ever had the misfortune to hear words spill out of Donald Trump's mouth, or read any of his typo-ridden tweets, you've probably thought to yourself: "Wow, this guy is not very intelligent".
He said that reaching out to congressional Democrats for help in getting immigration legislation passed is hard because "the Democrats don't want secure borders".
While Forbes noted Trump was talking about how he dealt with football team owners when he bought a New Jersey team in 1984, it's unclear whether that characterization of his business dealings applied to his other clients. It also said he had to be talked out of resigning.
"As the secretary of state said, this is a pretty ridiculous accusation and, frankly, I think it's beneath the secretary of state to weigh in on every rumor out there", Huckabee Sanders said.
Trump has suggested before that he was eying an executive order that would allow individuals to purchase insurance across state lines through so-called health associations, which Republican Senator Rand Paul has advocated.
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