Assistant Secretary for Health admiral Brett Giroir speaks as US President Donald Trump listens during a news conference on the novel coronavirus, COVID-19, in the Rose Garden of the White House in Washington, DC on April 27, 2020.

There's "no way on Earth" the U.S. can test 5 million people a day for the coronavirus, the government's top testing official said in an interview, just hours before President Donald Trump vowed that the country would be able to test that many people daily "very soon."

"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," Adm. Brett Giroir, assistant secretary of health who is in charge of the government's testing response, told TIME in an interview he gave Tuesday morning that was published later in the evening. The interview took place before Trump's eye-popping pledge about testing.

Speaking to reporters the following day, Trump denied having said there would be 5 million tests per day, but he added that he does believe there will, in fact, be 5 million tests per day at some point.

"Somebody came out with a study of 5 million people. Do I think we will? I think we will, but I never said it," Trump claimed during an event at the White House. "Somebody started throwing around 5 million. I didn't say 5 million," the president insisted, adding, "Well, we will be there. But I didn't say it. I didn't say it."

The U.S. will be able to test 8 million per month by May, Giroir told Time.

Giroir was responding to a new study's findings. Harvard University published a report last week that said the U.S. would need to ramp up testing capacity to at least 5 million tests a day by early June, and 20 million per day by late July, in order to reopen the economy. Giroir told TIME that the assessment is "an Ivory Tower, unreasonable benchmark," adding that it's not needed based on current modelling.

Trump, when asked at a news briefing about the 5 million figure later Tuesday, said, "We're going to be there very soon."