Even as Mr. Trump has promoted the drug, which is also often prescribed for patients with lupus, it has created rifts within his own coronavirus task force. And while many hospitals have chosen to use hydroxychloroquine in a desperate attempt to treat dying patients who have few other options, others have noted that it carries serious risks. In particular, the drug can cause a heart arrhythmia that can lead to cardiac arrest.

Dr. Megan L. Ranney, an emergency physician at Brown University in Rhode Island, said in an interview on Sunday night that she had never seen an elected official advertise a miracle cure the way Mr. Trump has.

“There are side effects to hydroxychloroquine,” Dr. Ranney said. “It causes psychiatric symptoms, cardiac problems and a host of other bad side effects.”

Dr. Ranney said that the drug could be effective for some patients, but that there was not nearly enough scientific evidence to support Mr. Trump’s claims.

“There may be a role for it for some people,” she said, “but to tell Americans ‘you don’t have anything to lose,’ that’s not true. People certainly have something to lose by taking it indiscriminately.”

Hydroxychloroquine has not been proved to work against Covid-19 in any significant clinical trials. A small trial by Chinese researchers made public last week found that it helped speed the recovery in moderately ill patients, but the study was not peer-reviewed and had significant limitations. Earlier reports from France and China have drawn criticism because they did not include control groups to compare treated patients with untreated ones, and researchers have called the reports anecdotal. Without controls, they said, it is impossible to determine whether the drugs worked.

But Mr. Trump on Sunday dismissed the notion that doctors should wait for further study.

“We don’t have time to go and say, ‘Gee, let’s take a couple of years and test it out,’ and let’s go out and test with the test tubes and the laboratories,” Mr. Trump said. “I’d love to do that, but we have people dying today.”