In response, the F.D.A. and Federal Trade Commission sent warning letters to at least seven companies warning them to stop advertising fraudulent cures and treatments for coronavirus, including essential oils, elderberry teas and colloidal silver supplements. The agencies cautioned that colloidal silver in particular is “not safe or effective” for any disease or condition. They said they were monitoring websites and social media to root out bogus products and that a task force has worked with major retailers and online marketplaces to remove dozens of listings for fraudulent coronavirus cures and treatments.

Americans already have a high level of anxiety about the spread of coronavirus, said Joseph Simons, the chairman of the F.T.C. “What we don’t need in this situation are companies preying on consumers by promoting products with fraudulent prevention and treatment claims,” he added.

Five of the major supplement industry trade groups applauded the government action and urged consumers to be wary of products making coronavirus-related claims. The industry has also lobbied the federal government and state and local officials to classify dietary supplement makers as “essential” in areas where there are shelter-in-place ordinances restricting nonessential commerce.

“I think the fact that we’re seeing this spike in sales tells us that consumers absolutely value their ability to use supplements,” said Steve Mister, the president and chief executive of the Council for Responsible Nutrition, an industry group.

The fastest selling supplements are those that have long been the subject of research on cold and flu relief, including zinc, vitamin D and elderberry extract. Zinc is thought to inhibit replication of the virus that causes the common cold. Some randomized trials have found that taking high doses of it may help to lower the risk of contracting a cold and potentially shorten its duration by 20 percent.

Supplementing with moderate doses of vitamin D has been shown in some trials to help lower the risk of contracting the cold and flu, but the effect is mainly seen in people who have very low or deficient levels. And a handful of small, industry-funded trials have found that elderberry extract can shorten the duration and severity of the cold and flu.

But the evidence for most of these supplements is not strong, and it’s not possible to extrapolate that they will help prevent or treat coronavirus because they have some efficacy against the cold and flu, said Kamal Patel, a nutrition researcher and the director of Examine.com, a large and independent database of supplement research. These viruses are quite different from one another. The coronavirus, for example, has a more severe impact on the lower respiratory tract and a longer incubation period compared to the viruses that cause colds and influenza.