Little spikes might turn into outbreaks with "really serious" consequences if there is a rush to reopen the US economy without following coronavirus guidelines, Dr Anthony Fauci, the country's top infectious disease expert, said Tuesday.

In a video testimony before a Senate committee, Fauci also cautioned that the mortality count of the COVID-19 pandemic in the US is likely higher.

He said that if states and cities disregard guidelines for safe reopening and prematurely open up, it "could turn the clock back", which not only would cause "some suffering and death that could be avoided, but could even set you back on the road to try to get economic recovery".

The hearing before the Health, Education, Labor and Pensions Committee came as more than two dozen US states have begun to lift their lockdowns as a first step toward resuming economic activities.

With mounting economic pressure and massive job losses, US President Donald Trump has supported states to reopen businesses. He tweeted Tuesday: "Our Testing is the BEST in the World, by FAR! Numbers are coming down in most parts of our Country, which wants to open and get going again. It is happening, safely!"

The testimony was attended at the Capitol by several mask-wearing committee members, with Senator Lamar Alexander, a Republican, chaired the hearing by video from the study in his cabin in Tennessee.

"Even under the best of circumstances, when you pull back on mitigation, you will see some cases appear," the director of the National Institute of Allergy and Infectious Diseases said.

Fauci, a key member of the White House Coronavirus Task Force, testified while self-quarantining after a White House staffer tested positive for the virus last Thursday.

"It's the ability and the capability of responding to those cases with good identification, isolation and contact tracing (that) will determine whether you can continue to go forward, as you try to reopen America," he said.

Fauci also warned that it is "entirely conceivable and possible" that a second virus wave will happen this fall.

The coronavirus outbreak has infected at least 1.3 million people in the US, with more than 80,000 deaths.

"If you think we have it completely under control, no we don't," Fauci said.

"If you look at the dynamics of the outbreak, we are seeing a diminution of hospitalizations and infections in some places such as in New York City, which has plateaued and is starting to come down, but in other parts of the country, we are seeing spikes," he said.

Asked if the US mortality count was correct, Fauci said "the number is likely higher. I don't know exactly what percent higher".

In commenting on Fauci's testimony, White House Press Secretary Kayleigh McEnany said, "I do want to stress, as the president has stressed, that we do want to reopen this country because there are consequences that run the other way when we stay closed down as a country."

J. Stephen Morrison, director of the CSIS Global Health Policy Center, said the American public remains uneasy about a premature lifting of shelter in place.

"There remains deep tension between public health safety on the one hand and a desire, understandable desire to exit the economic crisis and see a reopening of business and schools," he said Thursday.

James H. Stock, Harold Hitchings Burbank Professor of Political Economy at Harvard University, said that while reopening the economy is urgently needed, doing so in a way that leads to a second wave of deaths and a subsequent second shutdown could result in damage that is lasting and profound.

"Low-contact, high-value workplaces should be reopened quickly, and returning workers must feel safe," Stock suggested in a report submitted to a Brookings Institution discussion "Reopening the coronavirus-closed economy" Tuesday. "Some high-contact activities might need to be suspended indefinitely."