Trump's State Department chief made the remarks at an unscheduled news conference just after 11 a.m. Wednesday.
"I have never considered leaving this post," Tillerson said about what he described as "erroneously" reported stories.
"My commitment to the president remains strong."
Tillerson said he wanted to clarify the situation after a report from NBC News said he nearly left his cabinet post this summer after calling Trump a "moron," due to policy disputes.
In late July, Tillerson was in Texas while Trump addressed the Boy Scouts of America, and the secretary threatened not to return to Washington, according to the report.
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."
Minutes before Tillerson's statement, Trump posted to Twitter: "NBC news is #FakeNews and more dishonest than even CNN. They are a disgrace to good reporting."
"The vice president has never had to persuade me to remain as secretary of state because I have never considered leaving this post," Tillerson added.
When asked whether he had called Trump a "moron," Tillerson said he was "not from Washington" and "we don't deal with that kind of petty nonsense."
Tillerson worked for ExxonMobil for 42 years, including as chairman and chief executive officer from 2006 to 2016.
"I serve at the appointment of the president, and I am here for as long as the president feels I can be useful to his objectives," he said. "There is much to be done, and we are just getting started."
Last weekend, Tillerson said the administration was attempting to enter diplomatic talks with North Korea -- about which Trump remarked, "I told Rex Tillerson, our wonderful Secretary of State, that he is wasting his time trying to negotiate with Little Rocket Man. Save your energy Rex, we'll do what has to be done!"
"He loves his country. He puts Americans and Americans first," Tillerson said at Wednesday's news conference. "He's smart. He demands results wherever he goes and he holds those around him accountable for whether they've done the job he's asked them to do."