Dr. Fauci's critique resonated with Mr. Trump’s allies as well as his detractors. Sean Spicer, a former White House press secretary who during his tenure instituted “Skype seats” to allow smaller outlets without a Washington-based correspondent to ask questions during his briefings, said the idea still made sense.

Mr. Spicer, who attended a briefing last week in his new role as a host on the conservative site Newsmax and was called on by Mr. Trump, said “safety should be a massive factor” for the current format.

David Axelrod, a former top adviser to President Barack Obama, said accurate briefings during a crisis like the pandemic were critical. But he said the current state of play at the White House failed not only in accuracy but in optics.

“Not only is it unhealthy for the people in the room,” Mr. Axelrod said, “it sends a mixed message to the American people. Even if the briefings were held in the East or State Rooms, where people could be spaced, it would be better.”

Aides said Mr. Trump viewed the iconic room, with its blue seats and imposing White House seal behind the podium, as his best stage, one that gives him an imprimatur that cannot be replicated by any of his Democratic presidential opponents or governors like Andrew Cuomo of New York.

Mr. Cuomo has received high marks for an informative and emotional daily briefing he has been delivering from the State Capitol in Albany, which the president has closely watched and studied.

Some Trump advisers have struggled to find a good slot for the timing of the president’s briefings. Their preference would be to hold them earlier in the day, but Mr. Trump prefers getting closer to prime-time hours, and Mr. Cuomo’s briefings already dominate the mornings.