President Donald Trump is getting annoyed with Dr Anthony Fauci, the director of the National Institute for Health and Infectious Diseases, reported The New York Times.

Aides to the president believe Fauci takes "shots" at Trump in some interviews, while declaring his support for the president when talking to conservative media.

In a clip that went viral Friday Fauci covered his face with his hand in seeming exasperation as Trump riffed about the "deep state" conspiracy.

Fauci said he was instead trying not to choke on a throat lozenge.

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President Donald Trump is growing increasingly frustrated with Dr Anthony Fauci, the leading US expert on infectious diseases, according to The New York Times.

Fauci has in public appearances corrected false or misleading statements about the novel coronavirus made by the president, and expressed some frustration at the government's handling of the pandemic.

Fauci, the director of the National Institute for Allergies and Infectious Disease, is one of the leading public health experts in the coronavirus task force assigned by Trump to lead efforts to battle the pandemic.

But according to the Times report, aides to Trump are annoyed that, while praising the president in conservative outlets like Fox News, Fauci is taking "shots" at the president in print media.

On Sunday, in an interview published on Science magazine's website, Fauci was candid about his frustration at Trump's insistence of spreading misleading claims about the disease.

"I can't jump in front of the microphone and push him down. OK, he said it. Let's try and get it corrected for the next time," he told the publication, describing his limited power to influence the president.

However, he said that to Trump's "credit, even though we disagree on some things, he listens. He goes his own way. He has his own style. But on substantive issues, he does listen to what I say."

In daily briefings by the coronavirus task force, Fauci has rebutted claims made by the president. On Friday he said there was no scientific evidence to support a claim made by Trump in a tweet a day earlier that an antimalarial drug could prove effective against the coronavirus.

In a clip that went viral Friday, Fauci covered his face with his hand as though in exasperation, when Trump began to riff about the "deep state" conspiracy. Fauci has claimed that he was trying to suppress coughing on a throat lozenge.

Early Tuesday morning, Trump retweeted this video of the moment, but did not give any suggestion of what he meant by sharing the clip.

The president is rarely contradicted by aides and officials in public, and has so far tolerated Fauci's interjections.

The Times reported earlier on Monday that the president may be allowing him more leeway because of the approval in the media and from the public for his sober and fact-based assessments of the crisis.

However, the president's views on the measures required to fight the virus seem increasingly at odds with Fauci's advice.

On Monday Trump hinted that lockdown measures introduced to combat the spread of the virus could be lifted as soon as next week, in order to lift the US economy.

When asked at the coronavirus task force briefing Monday, where Fauci was not present, whether the doctor agreed with the lifting of restrictions, Trump responded: "He doesn't not agree with me."