Fauci had openly complained about being cited in a Trump re-election campaign advertisement that discussed the administration's pandemic response, and said in a CBS interview that he was not surprised Trump himself contracted Covid-19.
Trump, speaking in Las Vegas ahead of two rallies in Arizona, said Fauci “bombed” during television interviews but that it would be “a bigger bomb if you fire him”.
Fauci's office did not immediately respond to a request for comment.
Trump said Americans were fed up with pandemic restrictions.
“People are saying: 'Whatever. Just leave us alone.' They’re tired of it. People are tired of hearing Fauci and all these idiots,” said Trump, whose rallies include many supporters not wearing masks and standing shoulder to shoulder, at odds with the guidance of Fauci and other public health experts.
“Fauci is a nice guy. He’s been here for 500 years,” Trump said.
Republican senator Lamar Alexander issued a statement calling Fauci, who has been director of the National Institute of Allergy and Infectious Diseases since 1984, “one of our country’s most distinguished public servants”.
“If more Americans paid attention to his advice, we’d have fewer cases of Covid-19, and it would be safer to go back to school and back to work and out to eat,” Alexander said.