Assistant Secretary of Health Adm. Brett Giroir, the official leading the federal government's coronavirus testing response, told Time Tuesday “there is absolutely no way" the U.S. will be able to conduct 5 million coronavirus tests per day, contradicting comments President Trump made at a press briefing later in the day.

Why it matters: A Harvard University paper assessed that the U.S. would need to conduct 5 million tests daily by early June, and 20 million a day by late July, to reopen safely. But Giroir called the number “an Ivory Tower, unreasonable benchmark.” He said modeling projections did not call for it, nor could technology support it.

While the number of daily tests has increased recently to nearly 250,000, health experts say it's still not nearly enough to safely lift stay-at-home measures.

The most tests the U.S. has run in a day is 314,182 on April 22, according to the COVID Tracking Project.

What they're saying: Giroir told Time “there is absolutely no way on Earth, on this planet or any other planet, that we can do 20 million tests a day, or even five million tests a day.”

When asked at a press briefing later Tuesday if the U.S. could hit 5 million tests a day, Trump responded: “We’re going to be there very soon.”

Where it stands: Giroir said the U.S. has conducted 5.7 million tests total since the start of the year. He plans to do 8 million tests monthly by next month.