US Vice President Mike Pence and other top officials intervened to persuade Secretary of State Rex Tillerson not to resign during the summer as tensions rose between President Mr Trump and the nation's top diplomat, NBC News reports.
In July, Pence met with Mr Tillerson in an effort to ease growing discord over policy, NBC reported on Wednesday, citing 12 current and former senior administration officials and other people close to Mr Trump.
Their meeting came days after Mr Tillerson, in a session with Mr Trump's national security team and Cabinet officials at the Pentagon, openly criticised the President and reportedly called him a "moron", NBC said, citing three officials familiar with the incident.
Representatives for the State Department and the White House did not immediately respond to requests for comment on the NBC report.
Mr Tillerson, in late July, had weighed whether to return to Washington from a personal trip to Texas but was reassured after discussions with General John Kelly, now Mr Trump's chief of staff, and Defence Secretary James Mattis, the network reported, citing four people with direct knowledge of the exchanges.
Mr Tillerson said publicly in late July that he was "not going anywhere".
The White House declined to comment to NBC, and a State Department spokesman told the network Mr Tillerson did not consider quitting in July and did not call the president a moron.
"Wow, so many Fake News stories today. No matter what I do or say, they will not write or speak truth. The Fake News Media is out of control!" Mr Trump tweeted on Wednesday morning shortly after NBC published its report. It was not clear what stories Mr Trump was disputing.
Over the weekend, Mr Tillerson said the United States had direct channels of communication with North Korea to see if it was interested in dialogue in hopes of reducing tensions. The next day on Twitter, Mr Trump said Mr Tillerson was "wasting his time".
Mr Tillerson is not the only Cabinet official to have publicly diverged from the president on policy issues.
Mattis said on Tuesday the United States should consider staying in the Iran nuclear deal unless it was proven that Tehran was not abiding by the agreement or that it was not in the US national interest to do so.
Mr Trump has called Iran's 2015 deal with six world powers an "embarrassment".
Mattis has played down any tensions between Mr Trump and Mr Tillerson over their apparent split, most recently over North Korea.