President Trump said at a press briefing that he disagrees with Anthony Fauci's assessment that the U.S. is "just not there yet" in terms of reaching the testing capacity needed to reopen large parts of the economy.

Why it matters: Fauci is the nation's top infectious diseases expert and is among the most trusted voices on the White House's coronavirus task force.

The number of coronavirus tests being completed every day in the U.S. has increased in recent weeks, but experts say it still falls short of what is needed to relax stay-at-home orders.

A number of governors said this week that there are shortages of key testing ingredients like swabs and reagents that are preventing their states from meeting demand.

Driving the news: Fauci said in an interview with TIME magazine Thursday that “we are not in a situation where we can say we are exactly where we want to be with regard to testing."

“We need to significantly ramp up not only the number of tests, but the capacity to perform them, so that you don’t have a situation where you have a test but it can’t be done because there isn’t a swab, or because there isn’t extraction media, or not the right vial,” Fauci told TIME.

“I am not overly confident right now at all that we have what it takes to do that. We are doing better, and I think we are going to get there, but we are not there yet.”

What Trump's saying: "No, I don't agree with him on that. No, I think we're doing a great job on testing," the president said at Thursday's White House briefing, repeating his near-daily claim that the U.S. has tested more people for the coronavirus than any other country.

"As you know, and as I've said very times, we're very advanced in testing. Other countries are calling us to find out what are we doing."

"And by the way, in two weeks, you'll see numbers, and you'll see different forms of testing just like we came up with the Abbott laboratory machine, which gives it [to] you in five minutes, which everybody wants ... But as you know, we've done more testing than every other nation combined. And that's a big statement."

Go deeper: Governors contradict Trump's claims that states have testing capacity to reopen