A senior US health official set to testify on Tuesday before the US Senate will warn against the risks of reopening the economy too soon, saying it could lead to "needless suffering and death", the New York Times said.

The comments came as the United States has recorded more than 1.35 million infections and over 80,000 deaths, according to Reuters' figures, while worldwide the number is nearly 4.2 million infections and more than 285,000 deaths.

"If we skip over the checkpoints in the guidelines to 'Open America Again,' then we risk the danger of multiple outbreaks throughout the country," the newspaper quoted Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, as saying in an email.

"This will not only result in needless suffering and death, but would actually set us back on our quest to return to normal."

Fauci said the danger of trying to open the country prematurely was his major message for the Senate Health Education, Labor and Pensions committee at the meeting, the paper said late on Monday.

The National Institute of Allergy and Infectious Diseases did not immediately respond to a Reuters request for comment.

President Donald Trump's senior adviser and son-in-law Jared Kushner told Fox News the United States had crossed 9.30 million virus tests, with more than 394,00 done on Monday.

The rise in infections has put pressure on US efforts to boost testing capacity with health officials, including Fauci, having flagged the challenge of testing those in greatest need.