Dr Deborah Birx, the White House coronavirus response coordinator, also raised concerns with how the country's Centre for Disease Control and Prevention (CDC) has handled some of its data, including death toll.
However, Trump in recent past had said, "Our numbers are, essentially certified numbers".
In his first appearance on Capitol Hill in two months, Anthony Fauci delivered a cautionary message at odds with the rhetoric of President Donald Trump, who has pressed for rapid steps to rekindle the devastated economy.
On Monday Trump repeated the incorrect assertion that the USA was doing better at testing for the coronavirus than any other country.
"Of course", Fauci said.
"It's just - to me it's not an acceptable answer, especially when it comes to schools", Trump said.
While Fauci has become the trusted science voice for millions of Americans, Sen. "They're in great shape", he said, going on to suggest the benefits outweigh the risks for higher education institutions.
The Kentucky Republican then said, "Outside of New England, we've had a relatively benign course for this virus nationwide, and I think the "one-size-fits-all" that we're going to have a national strategy and nobody's going to go to school is kind of ridiculous".
"We have many candidates and hope to have multiple winners", Fauci added. "But if we don't, there would be problems".
Senator Kaine, who repeatedly cut Dr Fauci off from answering questions he posed, said the Covid-19 death rate in the USA was 45 times higher than in South Korea. Paul, who dismissed the scientist's conclusions, said, "I don't think you're the end-all".
Also testifying remotely before the committee will be Robert Redfield, the director of the Centers for Disease Control; Brett Giroir, assistant secretary for health at the Department of Health and Human Services; and Stephen Hahn, commissioner of the Food and Drug Administration.
"He wants to play all sides of the equation", Trump said of Fauci before emphasizing his confidence that the economy would quickly rebound from the coronavirus pandemic. "I think we need to be careful we're not cavalier in thinking children are completely immune to the deleterious effects". "Dr. Fauci is someone who feels strongly that the reopening can occur, but only if it's safe and you're following the White House guidelines and he reiterated that again and I think that's true".
"In the United States before Covid-19 millions didn't have it, and lacked access to health care".
New Jersey Governor Phil Murphy said on Tuesday he meant to announce some tentative moves toward reopening even though his state, by some measures, is now the most serious coronavirus danger zone in the US.
He mentioned a slowing in the growth of cases in hotspots such as NY, even as other areas of the country were seeing spikes.
But as of this week, the U.S. has tested only 2.75% of its 330m population, and no state has tested 10% of residents. "So when you look at the dynamics of new cases, even though some are coming down, the curve looks flat with some slight coming down".
The remarks came as the USA was debating whether it is safe for states to open up, prompted by a growing economic pressure and massive job losses amid concerns over a possible surge in coronavirus cases and fatalities if steps were not taken properly.
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