A week after appearing to project a more serious tone about the coronavirus, US President Donald Trump is back to pushing unproven claims that an anti-malaria drug is an effective treatment and challenging the credibility of the nation's leading infectious disease expert.

Dr Anthony Fauci, the director of the National Institute of Allergy and Infectious Diseases, pushed back on Tuesday, saying he will keep doing his job.

Numerous studies, meanwhile, have shown that the drug, hydroxychloroquine, is not an effective treatment for Covid-19, the disease caused by the coronavirus. And the US Food and Drug Administration recently withdrew an order that allowed the drug's use as an emergency treatment for Covid-19.

Yet overnight, after returning from a trip to North Carolina where he promoted efforts to develop a Covid-19 vaccine, Trump retweeted a series of tweets advocating for hydroxychloroquine.

The president also shared a post from the Twitter account for a podcast hosted by Steve Bannon, a former top White House adviser to Trump, accusing Fauci of misleading the public over hydroxychloroquine.

Fauci, a leading member of the White House coronavirus task force, pushed back on Tuesday during an appearance on ABC's Good Morning America.

"I go along with the FDA," said Fauci. “The overwhelming prevailing clinical trials that have looked at the efficacy of hydroxychloroquine have indicated that it is not effective in coronavirus disease."

It's not the first time Fauci has come under attack from Trump and those close to him.

The president's top trade adviser, Peter Navarro, who has clashed with Fauci over hydroxychloroquine, recently penned a scathing attack on the doctor that was published by USA Today. The newspaper later said the opinion piece did not meet its standards.

In recent nationally televised interviews, Trump himself has described Fauci as a bit of an alarmist and accused him of making mistakes in his coronavirus guidance to the American people.

Asked if he can continue to do his job when Trump continues to publicly question his credibility, Fauci said Tuesday he'll "press ahead no matter what” because of the stakes involved.

"I don't tweet. I don't even read them, so I don't really want to go there," Fauci said. "I just will continue to do my job no matter what comes out because I think it's very important. We're in the middle of a crisis with regard to an epidemic, a pandemic. This is what I do. This is what Ive been trained for my entire professional life and I'll continue to do it."

Asked about claims he's been misleading the public, Fauci said: "I have not been misleading the American public under any circumstances."