President Donald Trump said Tuesday the U.S. will "very soon" run 5 million coronavirus tests per day, even as the lack of testing remains an obstacle for many states anxious to reopen for business.

"We'll increase it, and it'll increase it by much more than that in the very near future," Trump said when a reporter asked if he's confident the U.S. will reach 5 million tests per day, as some health experts say would be required to "reopen" the country.

Speaking to the press the following day, Trump denied ever having said there would be 5 million tests per day, but he added that he does believe there will, in fact, be five million tests per day.

"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 on Wednesday. "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. is currently nowhere near conducting 5 million tests a day, and there is skepticism within the Trump administration itself about whether the country could hit that goal. Adm. Brett Giroir, who is running the administration's testing response, told Time magazine in an interview Tuesday morning, before Trump's remarks, that "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 5 million tests a day."

The most tests the nation has run on a single day was 314,182 on April 22, according to data compiled by the Covid Tracking Project. The U.S. has run just 5.7 million total Covid-19 tests since the beginning of the pandemic, according to the volunteer project designed to track testing data launched last month by The Atlantic.

That puts the nation woefully behind where its testing capacity needs to be. At the average rate of around 157,000 tests run a day in April, according to the project, it would take almost 6 years to test everyone in the U.S. — just once. Health-care workers and other first responders need to be tested often. New York state is requiring private companies that want to bring their employees back to work to test them frequently.