At his briefing on Friday, Mr. Trump said he was not aware of the government’s own latest forecasts, but aides said he had interpreted the decreasing death projection to mean that his health advisers may have been overly pessimistic.

The president cited the 60,000 estimated death toll as evidence of progress. “I think we’ll be substantially under that number,” he said of the earlier 100,000 forecast. “Hard to believe that if you have 60,000, you can never be happy, but that’s a lot fewer than we were originally told.”

But his public health advisers took a more cautious approach. “As encouraging as they are, we have not reached the peak,” Dr. Deborah L. Birx, the White House pandemic coordinator, said of the latest figures. She noted that without universal testing, experts were seeing only the most serious cases. “Is this the tip of the iceberg, or is this half the iceberg or three-quarters of the iceberg that we’ve seen to date?” she said.

Five administration officials said it was highly unlikely that Mr. Trump would extend the guidelines beyond April 30, adding that he would be more likely to find a way to announce some lifting of quarantine measures, even if it might not be a full flip-the-lightswitch reopening of the country.

Mr. Trump has been having conversations, both formally and informally, in recent weeks with business leaders like Michael Corbat, the chief executive of Citigroup, and Brian Moynihan, the chief executive of Bank of America, about how to support the economy and when it might be able to reopen.

Many of those discussions have been facilitated by Treasury Secretary Steven Mnuchin, who has fielded calls from executives like Stephen A. Schwarzman, the chief executive of Blackstone, looking for a road map to when a semblance of normalcy could return, although some people close to the discussions said that Mr. Schwarzman and Steven Roth, a real estate investor close to Mr. Trump, have not been aggressive as others.

Other business executives have gone through Jared Kushner, the president’s son-in-law and senior adviser. Paul Tudor Jones made an impassioned push to reopen the economy on a conference call organized by Mr. Kushner several weeks ago, these people said, and the investor Nelson Peltz was said to be influential in Mr. Trump’s since-aborted plan to begin reopening by Easter.