Trump's tweet of support for Tillerson followed a lunch that both men attended along with Defense Secretary James Mattis.
Trump: The media has been speculating that I fired Rex Tillerson or that he would be leaving soon - FAKE NEWS! He's not leaving and while we disagree on certain subjects, (I call the final shots) we work well together and America is highly respected again!
Earlier in the day, Tillerson, the 65-year-old former Exxon Mobil chief executive, called reports about his possible departure "laughable."
On Thursday, multiple news outlets reported that the White House has a plan to oust Tillerson and replace him with CIA Director Mike Pompeo. The change could take place within several weeks, The New York Times reported, though the newspaper noted that it was unclear if Trump signed off on it.
Trump on Friday said he and Tillerson have a good working relationship but noted that he has the "final" say in foreign policy decisions.
"He's not leaving and while we disagree on certain subjects, (I call the final shots) we work well together and America is highly respected again!" Trump wrote.
On Thursday, the State Department said Tillerson would continue with his scheduled duties.
Reports for months have painted a picture of a tense working relationship between the president and his top diplomat. In October, NBC News reported that Tillerson considered leaving the job and called Trump a "moron" during the summer.
The secretary of State then delivered a remarkable, unscheduled statement in which he insisted he "never considered leaving."
Later Friday, two administration officials confirmed to NBC News that R.C. Hammond, Tillerson's senior advisor for strategic communications, will leave mid-December. Hammond had been the only press aide accompanying Tillerson on trips.