Mattis has often publicly walked back some of Trump's more controversial statements on foreign policy, and the two have a strained relationship, veteran journalist Bob Woodward has reported in his book Fear.
In one episode reported by Woodward, Mattis described Trump as having the understanding of "a fifth- or sixth-grader" after a National Security Council meeting. In another episode, after Trump said he wanted to have Syrian President Bashar al-Assad assassinated, Mattis reportedly agreed but later told an aide, "We're not going to do any of that".
Mattis has denied making disparaging comments about Trump, and the President said last month that the retired general was "doing a fantastic job".
In the 60 minutes interview, Trump also described reports of chaos within his Administration as "so false," dismissing concerns about the rate of turnover among his top officials.
"I'm changing things around, and I'm entitled to. I have people now on standby that will be phenomenal. They'll come into the Administration. They'll be phenomenal," Trump said.
He said that while he was satisfied with the performance of certain members of his Administration, there are others "that I'm not thrilled with".
"Yeah, other people will go, sure," Trump said.
