Earlier, Tillerson denied a NBC News report that he came close to resigning this summer but was urged to stay in the job until the end of the year. Trump said he was "very honored" by the top U.S. diplomat's hastily scheduled Wednesday statement.
"Total confidence in Rex. I have total confidence," the president told reporters in Las Vegas, where he was meeting with first responders working the deadliest mass shooting in modern American history.
The NBC story, citing multiple high-level administration sources, said Tillerson referred to Trump as a "moron" in July following a meeting with the president's national security team. Tillerson did not personally deny that he used the term to describe Trump.
A State Department spokeswoman later said the secretary did not call the president a "moron."
Trump called the story "totally phony" and claimed NBC "just made it up." NBC, which shares a parent company with CNBC, stands by its reporting.
Since Tillerson took the post in February, mixed messages have repeatedly come out of the White House and the State Department. Trump has put less emphasis on the secretary of State's role than his predecessors did. The administration also proposed a major reduction in the agency's budget.
The apparent strain between the president and secretary of State comes amid major international crises, including a potential nuclear showdown with North Korea.
On Saturday, Tillerson said the U.S. had reached out to Pyongyang in an attempt to de-escalate tensions over its missile tests and nuclear explosions. But on Sunday, Trump tweeted that Tillerson is "wasting his time" trying to negotiate with North Korea.
Trump reportedly grew frustrated with Tillerson because of the slow pace in appointing staff at Foggy Bottom earlier this year. Tillerson elicited more of the president's ire when he was asked in August about Trump's values. The president had said some "very fine people" marched with the torch-bearing white nationalists in Charlottesville, Virginia.
"The president speaks for himself," Tillerson told Fox News at the time.
Disclosure: NBC and CNBC are owned by NBCUniversal, a division of Comcast.