Later, when the campaigns of former Vice President Joseph R. Biden Jr. and Senator Bernie Sanders of Vermont announced that staff members would work from home through March, Mr. Trump’s campaign, based in Arlington, Va., insisted it would remain open after a weekend deep clean.

It was only after Mr. Trump himself on Monday appeared to acknowledge the significance of the crisis and recommended that Americans avoid gathering in groups of more than 10 people that the campaign told staff members to work from home.

“While Americans can see that President Trump has been leading the whole-of-America coronavirus response, his campaign has been constantly evaluating the entire situation,” said Tim Murtaugh, a campaign spokesman. Now that it is working remotely, he added, the campaign has “pivoted to a virtual, digital approach, since we have vastly better data and a superior digital connection to voters than any other campaign.”

For now, Mr. Trump has been pleased with his regular White House briefing room appearances discussing the coronavirus, officials said, and views them as something of a rally replacement in a time of crisis. On Tuesday, he spoke for more than 90 minutes, about the length of an average Trump rally.

But the campaign is now facing an uncertain future.

A campaign aide who is related to Mick Mulvaney, the former acting White House chief of staff, fell ill last weekend after spending time at Mar-a-Lago, where the campaign held a fund-raising event. After showing symptoms, the aide was tested for the coronavirus, fearing she may have been exposed to a Brazilian official who tested positive for the virus just days after participating in meetings with Trump officials in Florida.

That has created a sense of concern and unease among campaign officials. It also raises questions about when the campaign will be able to start fund-raising in earnest again, and under what circumstances.

Dan Eberhart, a Republican donor who has been involved with Trump fund-raising efforts, said the president’s team has had the advantage of being well ahead in fund-raising as the Democratic race dragged into March.