Mr. Kushner rejected the concerns of governors and public health experts who said that testing remained woefully inadequate to justify reopening the country after weeks of lockdown. While Mr. Trump’s administration committed this week to helping states be able to test at least 2 percent of their populations each month, experts said that is a fraction of what is needed to map out how far the virus has spread.

“We’ve done more tests than any other country in the world, so we’ve got to be doing a lot of things right,” Mr. Kushner said.

Mr. Kushner did not address why the president for weeks played down the virus, comparing it to the ordinary flu, predicting that cases would go down to zero and suggesting that the virus would “miraculously” go away. People close to the White House have said that Mr. Kushner agreed with Mr. Trump early on that the Democrats and media were hyping the virus to damage the president, although Mr. Kushner’s allies have insisted that the always took it seriously.

In his interview on Wednesday, Mr. Kushner said May “will be a transition month” as states began reopening. “I think you’ll see by June a lot of the country should be back to normal,” he said. “And the hope is that by July the country’s really rocking again.”

Gilead said a drug study showed ‘positive data,’ but another study found no benefit to severely ill patients.

Gilead Sciences on Wednesday announced that the company “is aware of positive data” from a federal trial of its experimental coronavirus drug, remdesivir, even as a new study reported that the drug offered no benefit to severely ill patients in China.

Neither Gilead nor officials at the National Institute of Allergy and Infectious Diseases, sponsor of the federal research, provided further details about the trial sponsored by N.I.A.I.D., part of the National Institutes of Health.

President Trump is expected to discuss the findings at a White House briefing later today. In the past, Mr. Trump has hailed remdesivir as a potential “game changer,” despite spotty evidence.