But the F.D.A. has not approved any drugs for use in the treatment of coronavirus, and the drugs were already available, to treat malaria as well as rheumatoid arthritis and lupus. To date, the F.D.A. has not added the coronavirus to the list of illnesses for which the drugs are specifically approved. Then again, doctors have been free to use both old malaria drugs for any purpose deemed appropriate.

At the briefing on Thursday, Dr. Stephen M. Hahn, who has been the commissioner of the Food and Drug Administration for only three months, tended to walk back some of the president’s more inflated predictions that these drugs might vanquish the virus altogether.

He said Mr. Trump had asked the agency to look into chloroquine to fight the coronavirus, and that it was setting up a large clinical trial to evaluate the drug.

Some hospitals in the United States have already begun using the drugs for coronavirus patients, apparently reasoning that they may help and are unlikely to do harm. They are cheap and relatively safe. Laboratory studies have found that they prevent the coronavirus from invading cells, suggesting that the drugs could help prevent or limit the infection.

Not everyone can take the drugs: They are not safe for people who suffer from heart arrhythmia, or those with impaired kidneys or liver.

The University of Minnesota is conducting a study in which people who live with a coronavirus patient are being given hydroxychloroquine to find out if it can prevent the infection.

Dr. Hahn also said that the agency was allowing sick patients to use remdesivir, the not-yet-approved antiviral drug made by Gilead. Such so-called “compassionate use” programs allow patients to take unapproved, experimental drugs if they have no other options.