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More than 8,500 specimens have been tested for the coronavirus across the United States, according to the Centers for Disease Control and Prevention, a promising sign that testing is finally becoming more widespread in this country after a series of missteps.

But because multiple specimens are required from each individual, the number of actual patients who have been tested is likely far lower.

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"Most patients have at least two specimens taken. Many have up to three," said Kelly Wroblewski, infectious diseases director for the Association of Public Health Laboratories, which represents the 100 local and state public health laboratories recognized by the CDC to do this type of testing.

The CDC recommends getting an upper and lower respiratory specimen to confirm the presence of the virus, meaning a swab taken from either the nose or the throat and then a specimen taken from the lungs, Wroblewski said.

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And because the virus is new, labs have been doing "serial testing" in many cases, she said. That means they take multiple specimens over multiple days from a single patient to help researchers learn more about COVID-19, the illness the virus causes, and get a sense for when it's safe for patients to leave quarantine without spreading it to other people.

Health and Human Services Secretary Alex Azar has promised millions of tests will be made available throughout the U.S. by the end of this week. But he acknowledged Monday that he did not know how many patients had been tested so far.

“I could not give you a number of how many Americans have received a test," Azar said at a briefing of the White House coronavirus task force.

While it's not known exactly how many individuals have been tested, the U.S. still lags far behind other nations, which have already run tens of thousands of tests. In South Korea alone, more than 140,000 people have been tested.

The CDC reported that as of Monday afternoon, 3,698 specimens have been tested by CDC labs, and 4,856 specimens have been tested by U.S. public health laboratories, for a total of 8,554 specimens.

But now that technical glitches appear to have been ironed out with U.S. tests and the criteria for who can be screened has been expanded, the numbers are expected to grow.

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"We are absolutely at a point where we can do at least 10,000 patients a day, assuming two specimens, and probably more," Wroblewski said.

Private diagnostic companies LabCorp and Quest Diagnostics also recently announced the ability to run tests for the coronavirus. LabCorp is able to perform several thousand tests per day and is adding new equipment and staff to increase capacity, a spokesperson said.

Quest Diagnostics, which is expected to start testing for the coronavirus Monday, did not immediately return a phone call and email from NBC News on Tuesday.

Even more tests are rolling out at academic labs as well, including at Johns Hopkins University and UW Medicine.

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