Behind the scenes, Tillerson's relationship with the president has also reached a head; the two have clashed on issues of policy, and the president recently challenged Tillerson to an I.Q. test after reports that Tillerson called him a "moron".
Last month, Mr Trump told Mr Tillerson not to waste time seeking talks with Kim Jong-un.
Tillerson has often found himself at odds with the president on a range of issues, from withdrawing from the Paris agreement on climate change to North Korea and, at times, Iran, according to current and former USA officials and news media reports.
U.S. Secretary of State Rex Tillerson on Sunday minimized tensions with his boss, President Donald Trump, and brushed aside comments from an influential lawmaker, who compared Trump's undermining of his top diplomat to a public castration.
A Republican senator has accused Donald Trump of "publicly castrating" Secretary of State Rex Tillerson with his tweets about North Korea.
"I checked, I'm fully intact", Tillerson deadpanned.
US flew bombers over Korean peninsula late Tuesday: South Korea military
Mr Trump also mocked Kim Jong-un, calling the regime's leader "Rocket Man". The US bombers had taken off from the Andersen Air Force Base in Guam.
Tillerson is among the most senior officials in Trump's Cabinet and White House who remains in his job, after a series of high profile resignations and firings.
"I am fully committed to his objectives", Tillerson continued.
"The secretary puts out as many options for the president as he can. And so everything that I have witnessed, all was fine", she said. "How he wants to use his own skills tactically to push things toward change, I am there to help him achieve those". I go out and do the best I can to execute those decisions successfully.
"I think it's fake news, but if he did that, I guess we'll have to compare IQ tests", the president said, adding, "And I can tell you who is going to win".
"The president speaks for himself", Tillerson said at the time.
They men also disagreed on the nation's Afghanistan strategy, which was discussed in the July Pentagon meeting, though Trump was persuaded by Tillerson and Secretary of Defense James Mattis to maintain the United States' presence in the region. Sen.