US Secretary of State Rex Tillerson is not leaving, President Donald Trump tweeted on Friday, after US officials on Thursday said the White House had a plan for CIA Director Mike Pompeo to replace him.

"The media has been speculating that I fired Rex Tillerson or that he would be leaving soon - FAKE NEWS! He’s not leaving and while we disagree on certain subjects, (I call the final shots) we work well together and America is highly respected again!" Trump said on Twitter.

The tweet linked to a picture of Mr Tillerson being sworn in as secretary of state with Mr Trump and Vice President Mike Pence looking on.