For the second-straight day, Trump took to Twitter to deride the NBC News report, calling it "fake news." He said the secretary "never threatened to resign."
In an earlier tweet, Trump sounded off about media reports, though he did not specifically reference NBC. He asked why the Senate Intelligence Committee is not investigating "Fake News Networks" to see why "so much of our news is just made up."
NBC, which shares a parent company with CNBC, stands by its reporting.
The Thursday morning tweets came a day after the leaders of the Senate Intel Committee, Sens. Richard Burr, R-N.C., and Mark Warner, D-Va., gave updates on their probe into Russia's role in the 2016 election and possible collusion with the Trump campaign. They suggested the investigation would not wrap up until at least next year. Burr said the issue of collusion is still "open."
Trump has repeatedly lashed out about congressional and special counsel investigations into Russian election influence. He has called the probes politically motivated witch hunts.
On Wednesday, NBC News reported that Tillerson came close to resigning this summer but was urged to stay in the job until the end of the year. Citing multiple high-level administration sources, NBC said he referred to Trump as a "moron" in July following a meeting with the president's national security team.
At a hastily scheduled news conference, Tillerson said he "never considered leaving" the job. He did not deny calling the president a "moron," calling it "petty" to talk about it. A State Department spokeswoman later denied that he used the term.
Asked about Tillerson on Wednesday, Trump said he had "total confidence" in him. Trump accused NBC of making up the report.
Reports of tensions between Trump and Tillerson have repeatedly surfaced for months. The president and the secretary have sent mixed messages on some foreign policy issues, particularly the path to denuclearization of North Korea.
Tillerson also rebuffed Trump over his defiant response to violence at a white supremacist rally in Charlottesville, Virginia, earlier this year.
Disclosure: NBC and CNBC are owned by NBCUniversal, a division of Comcast.