But his efforts have been overshadowed - some would say undermined - by Trump's un-diplomatic style and his streams of taunting tweets stirring worldwide tensions. He didn't provide names. Political reporter Carol Lee said on Wednesday that she and her NBC colleagues "extensively reported" the story, speaking with a dozen sources.
He insisted, "I have never considered leaving this post".
Trump targeted two adversarial entities in one tweet, the Senate intelligence committee, which is now investigating Russian interference in the 2016 presidential election, and the news media. "It is #FakeNews. They should issue an apology to AMERICA!" he wrote.
"There has never been a consideration in my mind to leave", the top American diplomat told reporters. He characteristically betrayed little emotion, though sounded indignant as he responded to questions about whether he had ever called the president a "moron".
"My commitment to the success to our president and our country is as strong as it was the day I accepted his offer to serve as secretary of state", Tillerson said.
"Like holding uncomfortable press conferences after he finds out they've called him a moron", Colbert speculated.
"Tillerson was asked point blank if he called Trump a moron", tweeted author Brian Klaas.
Tillerson also sought to rebut a report that claimed Vice President Mike Pence had to talk him out of resigning. Tillerson was president of the organization from 2010 to 2012, according to his State Department biography.
"I am not going to deal with petty stuff like that".
"Rex Tillerson never threatened to resign", Trump tweeted.
Tillerson said Wednesday that reports suggesting otherwise are "erroneous".