In a phone call with an undercover F.B.I. agent, according to court records, Dr. Staley said he was selling antimalarial medication that “cures the disease,” and identified the medication as hydroxychloroquine.

“It’s preventative and curative,” Dr. Staley said, according to prosecutors. “It’s hard to believe, it’s almost too good to be true. But it’s a remarkable clinical phenomenon.” During the phone call, they noted, he also mentioned another antimalarial drug — mefloquine — that he said he would sell to the undercover agent if he ran out of hydroxychloroquine.

Dr. Staley, according to prosecutors, said both drugs would totally cure Covid-19, the disease caused by the new coronavirus, and that taking the treatment before getting sick would make one immune for at least six weeks. According to prosecutors, Dr. Staley guaranteed that the treatment would cure virus, though he later seemed to couch that statement, telling the undercover agent: “There are no guarantees in life. There are no guarantees of anything.”

When Dr. Staley was interviewed by the F.B.I. the following week, according to prosecutors, he said it “would be foolish” to tell patients that the treatments are a 100 percent effective cure for the coronavirus.

“We will not tolerate Covid-19 fraudsters who try to profit and take advantage of the pandemic fear to cheat, steal and harm others,” Robert S. Brewer Jr., the U.S. attorney for the Southern District of California, said in the statement. “Rest assured: those who engage in this despicable conduct will find themselves in the cross hairs of federal prosecutors.”