NEW YORK — Seven weeks have passed since the first U.S. case of coronavirus was announced, and the government is failing to account for what could be thousands of additional infections because of ongoing problems with testing.

“The system is not really geared to what we need right now,” said Dr. Anthony Fauci, the top infectious disease expert at the National Institutes of Health. “That is a failing. It is a failing, let’s admit it.”

The effort initially was hobbled by delays in getting testing kits out to public health labs, but the stumbles have continued, leading scientists to conclude that the virus has taken root in more places than government officials say.

U.S. health officials, for example, promised nearly a month ago to tap into a national network of labs that monitor for flu. That system is only just getting started.

Large-scale testing is a critical part of tracking the spread of infectious diseases and allocating resources for treatment. The lack of comprehensive figures means U.S. health providers could quickly be overwhelmed by undetected cases.

As of Thursday afternoon, the Centers for Disease Control and Prevention reported about 1,260 U.S. illnesses — a number that trailed independent researchers, who are adding reports from individual states more quickly.

But some experts believe any number based on test results of individual patients is a dramatic undercount. Researchers at Cedars-Sinai Medical Center in Los Angeles this week estimated that the true count of infections was close to 9,000 — about two weeks ago.

“I expect there are more infected individuals now,” said one of the researchers, Dr. Jonathan Braun. “This means that the level of disease in the U.S. is much greater than has been reported by actual testing.”

The problem, these experts say: The U.S. simply isn’t testing enough people.

There are no official numbers from the federal government on the country’s overall testing capacity. One of the only comprehensive estimates comes from Dr. Scott Gottlieb, the former FDA commissioner who is now a resident fellow at the American Enterprise Institute, a conservative think tank.

As of Thursday, his group estimated U.S. labs could process results for more than 20,000 patients per day. The figure is based on a combination of publicly reported information and historical estimates from government, private and academic labs.