The testing glitch appeared to have occurred in scaling up the manufacturing of test kits.

The kits had three components but some of the components were producing an inconclusive result for many public health labs using the test. On Thursday, the agency announced that labs with two of three working components could go ahead and use the C.D.C. tests, and it broadened the criteria for testing to include people who had traveled to countries with coronavirus infections in addition to China. But positive results still needed to be reconfirmed by the C.D.C. in Atlanta, and labs with only one working component could not conduct tests at all.

“Because of these limited resources, we could not get some of our patients tested,” said Dr. William Schaffner, an infectious disease specialist at Vanderbilt University Medical Center in Nashville.

Dr. Schaffner said he had a patient come in earlier this week who had developed symptoms of an upper respiratory infection after traveling to Italy, where a cluster of coronavirus infections has been observed. He referred the patient to the state laboratory, but officials there said she could not be tested because she did not meet the C.D.C. testing criteria at the time.

The testing limitations may have also prevented health officials from detecting cases earlier on in California, Oregon and Washington state, where people were found to have coronavirus infections despite having no history of travel to China or exposure to anyone with a confirmed infection. Those patients did not meet C.D.C.’s earlier criteria for testing. One person in Washington has since died of the coronavirus.

“If we had the ability to test earlier, I’m sure we would have identified patients earlier,” said Dr. Jeff Duchin, the health officer for public health in Seattle and King County, Wash., where the first death was reported on Saturday.

Both C.D.C. and the F.D.A. did have the option of adopting the test approved by the W.H.O., and public health experts said it was unclear why the agencies decided not to do so.

“In retrospect, it seems like a bad decision,” said one high-ranking C.D.C. official who requested anonymity and was not authorized to talk to the news media.