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Fact check: Trump falsely claims anybody who returns from Europe is being tested for coronavirus

Washington(CNN) President Donald Trump's Oval Office remarks on Thursday before a meeting with Irish Prime Minister Leo Varadkar were so thoroughly inaccurate it was a challenge to figure out which to fact check first.

We're still looking into some of Trump's claims. But here are the two we picked as most egregious:

Trump falsely claimed anybody coming into the US from Europe is being tested for the coronavirus

When a reporter noted that an American could bring back the coronavirus even with Trump's new travel restrictions on some European countries, Trump said, "Sure. But we have them very heavily tested. If an American is coming back or anybody is coming back, we're testing. We have a tremendous testing set up where people coming in have to be tested."

Facts First: It's not true that Americans or others returning from Europe "have to be" tested for the coronavirus -- and no system is being set up to actually test these returning travelers.

Instead, they will be funneled to specific airports and put through an inspection known as "enhanced screening," which cannot prove whether someone has the virus. Previous US airport screening for the coronavirus has involved temperature checks, questions about travelers' health and travel history, and an inspection for symptoms like a cough or breathing trouble.

At CNN, we start with the facts. Visit CNN's home for Facts First.

The administration's statements about the enhanced screening for travelers from Europe made no mention of coronavirus tests being conducted.

Trump falsely claimed testing has been "going very smooth"

Trump was asked about a case in which a doctor in Houston reported being unable to obtain permission to get a patient tested despite the patient having "symptoms of something" and having tested negative for the flu.

Trump responded that this was a mere "one case" and that "frankly, the testing has been going very smooth." He also claimed: "If you go to the right agency, if you go to the right area, you get the test."

Facts First: It's simply not true that testing has been going smoothly or that, as Trump suggested, it's simple to get a test by contacting the proper authorities.

Health officials in states around the country continue to report a shortage of tests and other problems. Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, told Congress on Thursday: "The system does not -- is not really geared to what we need right now ... that is a failing. It is a failing, let's admit it."

Dr. Fauci said, "The idea of anybody getting it easily the way people in other countr(ies) are doing it: we're not set up for that. Do I think we should be? Yes. But we're not."

Some of the tests initially shipped to states by the Centers for Disease Control and Prevention, after the CDC decided to develop its own test, were flawed, and federal obstacles have prevented other labs from quickly deploying their own tests. There are now concerns about a potential shortage of chemicals and materials needed for the tests.

The federal government originally set strict criteria for who could get a test. While the criteria were eventually relaxed to allow anyone with a doctor's authorization to get tested, the lack of tests available to doctors and local authorities has kept the number of completed tests low.

Lawmakers from both parties expressed frustration on Thursday about why the US is conducting far fewer tests than other countries, such as South Korea. Republican Sen. James Lankford of Oklahoma told CNN that Trump "should stop saying" that anyone can get a test if they want one.

"That is not accurate right now. People should stop saying if you want a test, you should get a test right now. That's not here at this point," Lankford said.

Haley Byrd, Lauren Fox, Manu Raju, Ted Barrett and Tara Subramaniam contributed to this article.
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