US President Donald Trump has said he has no plan to replace Secretary of State Rex Tillerson, though he acknowledged disagreements with the latter on certain subjects.

“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 wrote on Twitter on Friday, Efe news reported.

That was the President’s first public response after The New York Times quoted anonymous sources saying that Trump wanted to replace Tillerson with CIA director Mike Pompeo.

Tillerson also made his first statement on Friday in that regard and said the news is “laughable,” but avoided any mention of whether he has discussed the matter with the president.

“It’s laughable. It’s laughable,” he responded earlier to a question about how he’s handling the matter and what he’ll do about news that the White House seeks his resignation.

The news was repeated later by numerous US media including CNN and The Washington Post, also quoting anonymous sources.

Tillerson gave his terse reply about the matter at the State Department while welcoming Libyan Prime Minister Fayez al-Sarraj.

On Thursday, State Department spokeswoman Heather Nauert said that White House Chief of Staff John Kelly told Tillerson it wasn’t true that Trump plans his ouster within the coming weeks or months.

Questioned insistently about the matter during her daily press conference, Nauert defended Tillerson by saying he’s “committed to doing this job”.

She added, however, that the top diplomat “does serve at the pleasure of the president”.

Asked if Tillerson would fight to keep his job despite all the rumors going around, the spokeswoman said she’d rather not get involved in such speculation.

She acknowledged that Trump and Tillerson “have certainly had areas of disagreement” that are well-known, and gave as an example their opposite positions on climate change.

At a parallel press conference, White House spokeswoman Sarah Huckabee Sanders avoided giving a “yes” or “no” answer to the question of whether Trump has confidence in Tillerson.

“When the president loses confidence in somebody they will no longer be here,” was all Sanders would say.

As for Tillerson’s future, Sanders said that he and the president “are continuing to work together to close out what we’ve seen has been an incredible year.”