Mr Tillerson's reported disenchantment with the president came around the time Mr Trump gave a controversial political speech to the Boy Scouts of America, an organisation which Mr Tillerson once headed.
A reporter asked Tillerson point blank about the report that he called the president a "moron".
The report also said Vice President Mike Pence "counseled Tillerson ... on ways to ease tensions with Trump, and other top administration officials urged him to remain in the job at least until the end of the year".
There have been rumors in Washington for months that Tillerson, the former CEO of oil giant Exxon Mobil, was frustrated with Trump administration policies on a range of domestic and worldwide issues.
We've all called our boss a moron at some point in our lives - either to their face or otherwise - but we are rarely called before a press conference in order to clear up the matter. "I'm not gonna deal with petty stuff like that", he said.
Tillerson delivered the announcement from the State Department Wednesday, saying reports that he'd threatened to leave were untrue.
"This is what I don't understand about Washington", he said. "And I'm just not going to be part of this effort to divide this administration".
Tillerson did, however, lob some compliments Trump's way.
He confirmed that he would present President Donald Trump with several options on the nuclear deal with Iran ahead of a deadline on October 15 to testify whether Iran was bound by the agreement. He puts America and Americans first.
The White House was not immediately available for comment when contacted by CNBC and declined to comment on the record to NBC News for the story.
Mr Pence, in a statement, said he never discussed the prospect of the Secretary of State resigning. "He's smart. He demands results wherever he goes".
A State Department spokesman earlier told NBC that Tillerson did not call the president a moron and denied that the secretary considered resigning over the summer.