Last week the New York Times reported that Mr Tillerson was astonished at how little Mr Trump grasps the basics of foreign policy.
"Rex Tillerson never threatened to resign".
"I'm not undermining", Trump told Forbes.
Vanity Fair claimed Mr Trump is growing increasingly frustrated with his chief of staff, John Kelly.
In a televised interview with former Arkansas Gov. Mike Huckabee that aired Saturday night, Trump also wouldn't say if the United States was planning to get rid of the Iran deal.
U.S. Secretary of State Rex Tillerson looks at President Donald J. Trump during a ceremony to commemorate the Sept. 11, 2001 terrorist attacks, at the Pentagon in Washington, Sept. 11, 2017.more +.
Tillerson isn't the first to say it, and he'll be far from the last to make this point.
In the Forbes interview, conducted on Friday, Trump responded to criticism that he's undermined his secretary of state through his often provocative tweets that have interfered directly with ongoing diplomatic efforts.
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. But the secretary of state notably did not deny calling the President a "moron" and privately, sources tell CNN, Trump fumed at his secretary of state's comment. "He said he called him an f***ing moron".
"So much of our news is just made up-FAKE!"
White House Press Secretary Sarah Huckabee Sanders told reporters during a presser of her own that Tillerson didn't need to.
Trump also said he would be acting on health care soon, saying: "I will be using the power of the pen to give great HealthCare to many people - FAST". It was fake news.