“People count on being able to get their prescription drugs — they go to the drugstore counter and they expect the druggist to have what they need, and pay for it, and leave,” she said. “So what stands out to me is how many holes there are in this, how many unanswered questions there are.”

The F.D.A. has said it is closely monitoring about 20 products where the manufacturers rely solely on China for their finished products or active pharmaceutical ingredients. Dr. Hahn said Thursday that the drugs being monitored are considered “noncritical drugs.”

Hospitals have struggled for years with shortages of hundreds of critical drugs, many of them staples of medical care that have been on the market for decades. In 2017, Hurricane Maria damaged many pharmaceutical factories in Puerto Rico, closing them for weeks and leading to supply problems, including a shortage of saline bags made by Baxter. Problems with manufacturing quality have caused other shortages, including a global shortfall of valsartan, a widely used blood pressure drug.

Erin Fox, a drug shortage expert at the University of Utah, said, “When the F.D.A. tells the American public that there is a shortage without disclosing the specific drug, this only creates fear and panic, which is unacceptable in the current situation.”

The F.D.A. frequently cites companies’ proprietary reasons for why it does not disclose certain information, including the names of specific drugs when companies are cited for manufacturing problems, or details about clinical trials, Dr. Carome said. “Those are examples where I think it’s an overuse,” he said.

Ilisa Bernstein, who was a top compliance official at the F.D.A. until last fall and is now a senior vice president at the American Pharmacists Association, said the agency must maintain a balance. “Pharmacists want transparency, they want to be able to have the information that’s needed so they can better care for their patients,” she said. “But behind the scenes, I know the F.D.A. is working hard to figure out what the impact will be on the availability of that product.”

Representatives for several drugmakers have said they have several months’ supply of pharmaceutical ingredients, but some have acknowledged that if problems persist, they could encounter trouble. This week, Richard Saynor, the chief executive of Sandoz, the generic manufacturing arm of the drug giant Novartis, said in a LinkedIn post that “while we think we have solid levels of safety stock at my company, it is hard to predict how the situation will evolve further as the virus spreads to more and more countries.”