He was pushed out after less than eight months after numerous conflicts with Ivanka Trump, the president's elder daughter, and Jared Kushner, her husband and Mr. Trump's senior adviser.
Trump's comments come less than a week after his personal lawyer sent a cease-and-desist letter to the publisher and author of a book featuring an interview with former chief strategist Steve Bannon and a number of other members of the administration.
What is the Trump link? It also covers only Bannon's role on Trump's campaign, as opposed to events that occurred during the presidential transition or while Bannon served as a top aide to Trump in the White House.
The relationship between Mr Tillerson, a former oil executive, and Mr Trump has not always been strong but, in response to rumours he may be shown the door, Mr Tillerson said: I intend to be here for the whole year.
Mr. Bannon and Mr. Trump joined hands in August 2016, even as the latter's campaign was floundering.
But the president had sharp criticism for Bannon, accusing him of unfairly taking credit for his election win.
The session will reportedly focus on Bannon's involvement during the campaign period.
Bannon To Be Interviewed By House Intel For Russia Probe
What about his White House stint? Burck is not representing Bannon in the Mueller probe. "It becomes relevant, because many of us who read the book, and I read the book, are trying to understand where the White House denies it, well what's true and what's not true?"
Another possible avenue for Mr Bannon already is closed. He has long gleefully engaged in the culture wars that animated Bannon, targeting campus leftists and establishment Republicans with glee. Then began the setbacks. This is the first time a Democrat has won a senate seat in the deeply conservative state of Alabama in 25 years.
On Tuesday, Trump met with a bipartisan team in the nation's capital to discuss comprehensive immigration reform and amnesty for undocumented immigrants, of which Bannon was an outspoken critic.
But applying this rule that when push comes to shove Trump ultimately only cares about himself and his family also helps explain why Bannon's demise does not mean the end of Trumpism.
"When I write emails seeking interviews, my word choice is to say, 'I will treat the individual with dignity and respect.' I never go so far as to say, 'Let me humanize".More news: White House: There's Likely No Way Back for Bannon