Does the United States really have the capacity to ramp up its efforts and produce 1 million coronavirus tests by the end of this week, as the head of the Food and Drug Administration promised Monday during a White House briefing?

The figure includes orders for commercial tests that companies said were still weeks away from approval, and public health laboratories said their capacity doesn’t come close to that.

In remarks Monday, Dr. Stephen Hahn, the FDA’s commissioner, said actions taken by the agency to allow private labs and companies to begin making their own tests would greatly expand the capacity to test.

“With this new policy, we have heard from multiple companies and multiple academic centers, and we expect to have a substantial increase in the number of tests this week, next week and throughout the month,” Hahn said in a press briefing Monday. “There will be — the estimates we’re getting from industry right now, by the end of this week, close to a million tests will be able to be performed.”

The agency said afterward that Hahn was taking into account the anticipated, increased production of test kits by an outside manufacturer, Integrated DNA Technologies, which is now selling kits to the federal government and other buyers. But that would not increase the capacity of individual labs to perform the tests.

Hahn repeated the estimate in testimony Tuesday at a Senate committee hearing, where he told Sen. Patty Murray, D-Wash., that, although “this is a dynamic process,” the federal government was working with private companies to ship about 2,500 test kits to labs by the end of the week.

“That should give us the capacity, in the hands of laboratories once they validate, to perform up to a million tests,” he said at the hearing.

The Association of Public Health Laboratories, which represents state and local government laboratories around the country, has said that its labs would be able to conduct about 10,000 tests a day when all of its 100 members that can perform testing are running. Scott Becker, chief executive of the lab association, said Monday that labs can run about 100 tests per day. As of Monday, he said fewer than half of those labs were able to do so.

Hahn and White House officials have been trying to address the lag in testing caused by botched test kits that were rolled out by the Centers for Disease Control and Prevention early last month and that agency’s enforcement of strict testing criteria.

But as the coronavirus spread in Washington state and California and has popped up in the Northeast and Florida, state and federal lawmakers have clamored for expedited tests and the authority to conduct their own. So far, more than 100 people in the United States have been sickened, and at least six have died.

Public health experts have become concerned that the lack of adequate testing in several states has led to community transmission and warned there may be many undetected cases that could lead to further infections.

New York state’s public health lab, which was one of the first to receive emergency approval for its own testing, set a goal of conducting 1,000 tests a day statewide, according to a statement by Gov. Andrew Cuomo.

A handful of private companies have said they are working on a test for the virus, but none are yet available in the United States. Hologic said in a statement Monday that it expected to apply for approval on an emergency basis “in the coming weeks.”

Another company, Cepheid, has said it does not expect to get emergency approval from the FDA for its test before April. Dr. David Persing, the company’s chief medical officer, said last week that the company still wanted to ensure its test was accurate. “We are moving aggressively,” he said.

On Monday, Darwa Peterson, a Cepheid spokeswoman, said the FDA policy to allow more labs to conduct tests hadn’t changed the company’s timeline.

“We still need to optimize and validate our tests because commercial vendors are held to a high standard,” she said.

Qiagen, another company working on testing, said Tuesday that it expected FDA approval later this month but that it was still gathering data and testing its product, noting that “this does take some time.”

Hahn was not the only Trump administration official to promise radically expanded testing. Over the weekend, Vice President Mike Pence made similar claims, appearing on television to say that more than 15,000 test kits — which contain materials to test between 700 to 800 samples — were being shipped to labs.

In fact, the CDC said Sunday it had shipped about 47 such kits.

A spokeswoman for the Health and Human Services Department said Monday that about 3,600 specimens had been tested since the start of the outbreak. Close to 500 people had been tested as of Sunday, but an updated number was not provided. On Monday, as the testing controversy continued, the CDC removed its data on how many people had been tested from its website.

Other countries, like South Korea, are testing thousands of citizens per week, but in the United States testing has been more limited. The CDC began shipping test kits to labs around the country in early February, but a manufacturing problem led the agency to tell most states not to use the kits, severely limiting the country’s testing capacity for weeks.

Stringent testing criteria also tied the hands of infectious disease doctors around the country, who have said they were frustrated that they were not allowed to test a broader group of patients who displayed potential symptoms of the new virus. Last week, the CDC loosened its criteria and began shipping new test kits to labs around the country.

During a CDC news briefing Saturday, Dr. Jeff Duchin, public health officer of the Seattle and King County Public Health agency, which has been dealing with Washington state’s outbreak, said the death of a man in his 50s who had coronavirus was only identified because the Washington state public health lab had just recently acquired test kits.

“If we had the ability to test earlier, I’m sure we would have identified patients earlier in the community,” he said.

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