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Trump made the claim Friday in an interview with Forbes magazine, days after NBC News first reported that Tillerson called the president a "moron" after a July 20 meeting at the Pentagon. The Forbes interview was published online Tuesday.
"I think it's fake news, but if he did that, I guess we'll have to compare IQ tests," Trump told Forbes magazine. "I can tell you who is going to win."
The rising tension between Trump and Tillerson was highlighted last week after NBC News reported that Tillerson considered resigning over the summer after Trump delivered a politically charged speech to the Boy Scouts of America at their annual Jamboree. The head of the Boy Scouts later apologized for Trump's remarks.
Tillerson denied he ever considered resigning at a news conference last week, but did not deny calling the president a moron, instead categorizing the situation as petty.
“This is what I don’t understand about Washington,” Tillerson said on Wednesday. “I’m not from this place, but where I come from, we don’t deal with that petty nonsense.”
State Department spokeswoman Heather Nauert later denied the report, saying that Tillerson “does not use that language to speak about anyone.”
Several other news outlets subsequently confirmed the NBC News report, including The Washington Post and CNN.
Still, Trump claimed last week that the report was fabricated.
"It was fake news, it was a totally phony story," Trump said on Wednesday. "It was made up by NBC. They just made it up."
He added that he has "total confidence in Rex."
Tillerson, 65, has served as secretary of state since shortly after Trump took office in January. Before assuming office on Feb. 1, Tillerson worked as chairman and chief executive officer of oil and gas giant ExxonMobil.