The White House said on Monday that President Donald Trump was not firing US infectious disease expert Dr Anthony Fauci, despite his retweet of a supporter's #FireFauci message.

"This media chatter is ridiculous - President Trump is not firing Dr Fauci," said White House spokesman Hogan Gidley. "Dr Fauci has been and remains a trusted adviser to President Trump."

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Trump on Sunday retweeted a call to fire Fauci after the scientist said lives could have been saved if the country had shut down sooner during the novel coronavirus outbreak.

The message, "time to #FireFauci", was from a former Republican congressional candidate who cited Fauci's comments during a television interview.

The Republican president in the past has repeated critical tweets of officials or enemies rather than make the criticism himself. The retweet fueled speculation Trump was running out of patience with the popular scientist and could conceivably fire him.

Fauci has assumed national prominence as a leader in the fight against the coronavirus. He has contradicted or corrected Trump on scientific matters during the crisis, including whether the anti-malaria drug hydroxychloroquine is effective against it.

Fauci was asked on CNN's "State of the Union" about a New York Times report documenting early warnings issued to the White House about the novel coronavirus. The scientist acknowledged shutting the country down sooner could have saved lives, but cautioned that a number of factors were involved.

"Obviously, it would have been nice if we had a better head start, but I don't think you could say that we are where we are right now because of one factor," Fauci said. "It's very complicated."

NIH National Institute of Allergy and Infectious Diseases Director Anthony Fauci speaking as US President Donald Trump listens during a news conference in the Rose Garden of the White House [File: Al Drago/Reuters]

Fauci said later on Monday that Trump listened to his advice when he recommended that mitigation efforts be taken to stop the spread of the coronavirus.

Already a target of the far right for his contradictions of Trump, Fauci drew more opprobrium after the comments.

Trump also denounced the New York Times story in several tweets on Sunday, calling it "A Fake", without elaborating

Last week, during the daily White House coronavirus briefing, Trump stepped in and prevented Fauci from answering a question about hydroxychloroquine.

Fauci, 79, has led the federal infectious disease agency since 1984 under Republican and Democratic presidents. Republican George W Bush honoured him with the Presidential Medal of Freedom in 2008.

Some polls during the public health crisis have shown Americans trust him more than Trump.

Trump said during his Monday evening coronavirus briefing that he believes Fauci is a "wonderful guy".