Private companies and academic laboratories have been pulled in to develop and validate their own coronavirus tests, a move to get around a government bottleneck after a halting start, and to widen the range and number of Americans screened for the virus, Dr. Stephen Hahn, the commissioner of the Food and Drug Administration, said Monday at a White House briefing…

In the briefing, which was conducted by phone, the officials said that only 337 additional C.D.C. test kits were made available for distribution on Tuesday and Wednesday, according to two people on the call and the person briefed on the discussion who were not authorized to discuss it publicly. Each of those tests would cover about 350 people, officials said.

The officials added that they hoped that a private manufacturer could step in and provide 2,500 more kits by the end of the week. A spokesman for the Department of Health and Human Services said that public health labs currently can test 15,000 people, and could test up to 75,000 by the end of the week, numbers that fall well short of what Dr. Hahn indicated private labs could handle.