And while there is no specific treatment for the rapidly spreading infections, insurers have not expanded coverage for anyone, including the more seriously ill who need hospitalization. Almost all private health plans include hospital coverage, with patients in different plans left to pay different amounts of the bill, and that arrangement is intact in the era of covid-19, the disease caused by the virus.

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“We haven’t agreed to waive out-of-pocket costs for treatment,” said Kristine Grow, a spokeswoman for America’s Health Insurance Plans, the industry’s main trade group.

The president’s misstatements reflect confusion about the patchwork response to efforts to ensure that Americans’ inability to afford testing is not a hurdle — a critical matter when knowing who has the virus is crucial to slowing its spread. Those misstatements were repeated Thursday morning by the director of the Centers for Disease Control and Prevention testifying on Capitol Hill.

Until very recently, when only the CDC and then public health labs could perform the test, the government paid for the test itself, but not for the expense, say, of going to an emergency room to get tested.

The scenario is more complicated now that private testing companies have started to get involved. One of the largest, Quest Diagnostics, said Monday that doctors and other health-care providers could order the test.

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“We anticipate we will have performed several thousands of tests for patients by the end of the week . . . and expect to perform tens of thousands of tests within the next weeks,” the company said in a statement.

The people at greatest risk of finding a coronavirus test unaffordable are the 27 million uninsured Americans. And some of them may be especially vulnerable to infection, working in low-wage jobs such as food service that come without health benefits and exposure to the public.

No one is keeping complete tabs on how many people are getting tested across the country, so there is no information on how many of them lack health coverage.

Quest said in its statement that it had not finalized a price for those who are uninsured. “We have not yet finalized our uninsured patient price,” adding, “Our goal is to enable broad access.”

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A spokeswoman for another major company, LabCorp, said the company has been providing its test to doctors for the past week and testing specimens since last Friday. The spokeswoman, Pattie Kushner, said the company expects the federal government will probably pay $51 per test for Medicare patients, but she did not say what the price would be for uninsured customers.

People covered by most private insurance companies may see a test price on their benefits explanations, but they will not actually have to pay anything for the service. One by one in recent days, each of the nation’s major insurance companies issued public guarantees that they will cover the costs, and a group of industry leaders renewed this promise during a meeting Tuesday with Vice President Pence.

It is less clear whether testing costs are being covered by a relatively small slice of the industry that Trump administration health officials have been promoting: short-term health plans, as well as health plans sold to groups of individuals and associations. Both types are inexpensive because they offer skimpy benefits.

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On Thursday, the Internal Revenue Service issued a notice that private health plans with high deductibles — increasingly common across the country — can eliminate those deductibles for services related to the coronavirus without risking their tax status. The IRS notice said this refers to both testing and treatment.

The government’s largest public insurance programs, Medicare and Medicaid, are also covering the cost of testing, and federal health officials have recently been publicizing that fact.

At a congressional hearing Thursday, Robert Redfield, the CDC’s director, further muddled the administration’s message about paying for services related to the new virus.

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At one point during the House Oversight and Reform Committee hearing, Rep. Ayanna Pressley (D-Mass.) asked Redfield, “Will the cost of testing be covered?” He replied, “Cost of testing will be covered.”

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“And what about treatment?” Pressley asked. Again, Redfield replied, “Cost of treatment will be covered,” even though neither private nor public insurers have said they will pay the entire cost of care related to the virus.

Later during the hearing, Rep. Katie Porter (D-Calif.) reminded Redfield that she and House colleagues had asked him last week to use CDC authority to provide for testing and treatment at no cost, regardless of whether patients are insured.

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“Will you commit to invoking that and to provide testing for every American?”

He repeatedly declined to commit, saying that the CDC is collaborating with the Department of Health and Human Services to “operationalize” their response.

Porter persisted. “You can make that commitment now,” she said, demanding a response. “My answer is yes,” Redfield finally replied.

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But as the hearing was ending, Redfield took that back, saying the administration “is currently examining all avenues” for the uninsured to afford tests and treatment. In the meantime, he recommended that people go to community health centers.