On the afternoon of Feb. 24, President Donald Trump declared on Twitter that the coronavirus was “very much under control” in the United States, one of numerous rosy statements that he and his advisers made at the time about the worsening epidemic. He even added an observation for investors: “Stock market starting to look very good to me!”

But hours earlier, senior members of the president’s economic team, privately addressing board members of the conservative Hoover Institution, were less confident. Tomas J. Philipson, a senior economic adviser to the president, told the group he could not yet estimate the effects of the virus on the U.S. economy. To some in the group, the implication was that an outbreak could prove worse than Philipson and other Trump administration advisers were signaling in public at the time.

The next day, board members got another taste of government uncertainty from Larry Kudlow, the director of the National Economic Council. Hours after he had boasted on CNBC that the virus was contained in the United States and “it’s pretty close to airtight,” Kudlow delivered a more ambiguous private message. He asserted that the virus was “contained in the U.S., to date, but now we just don’t know,” according to a document describing the sessions obtained by the New York Times.

The document, written by a hedge fund consultant who attended the three-day gathering of Hoover’s board, was stark. “What struck me,” the consultant wrote, was that nearly every official he heard from raised the virus “as a point of concern, totally unprovoked.”

U.S. stocks were already spiraling because of a warning from a federal public health official that the virus was likely to spread, but traders spotted the immediate significance: The president’s aides appeared to be giving wealthy party donors an early warning at a time when Trump was publicly insisting that the threat was nonexistent.

Interviews with eight people who either received copies of the memo or were briefed on aspects of it as it spread among investors in New York and elsewhere provide a glimpse of how elite traders had access to information from the administration that helped them gain financial advantage during a chaotic three days when global markets were teetering.

The memo appears to have overstated the gravity of some administration officials’ warnings to the group and included dire projections from the CDC, without clear attribution, that do not appear to have come from the gathering.

But the memo’s overarching message — that a devastating virus outbreak in the United States was increasingly likely to occur, and that government officials were more aware of the threat than they were letting on publicly — proved accurate.

To many of the investors who received or heard about the memo, it was the first significant sign of skepticism among Trump administration officials about their ability to contain the virus.

“Short everything,” was the reaction of the investor.

The memo was written by William Callanan, a hedge fund veteran and member of the Hoover board, a research institution at Stanford University that studies the economy, national security and other issues.

Callanan described the Hoover briefings in a lengthy e-mail he wrote to David Tepper, the founder of the hedge fund Appaloosa Management, and one of his senior lieutenants about the level of concern among U.S. officials over the spread of the virus domestically. In the e-mail, he also touched on how ill-prepared health agencies appeared to be to combat a pandemic.

Inside Appaloosa, the e-mail circulated among employees, who in turn briefed at least two outside investors on the more worrisome parts of Callanan’s e-mail, according to people who received those briefings.

Those investors in turn passed the information to their own contacts, ultimately delivering aspects of the readout to at least seven investors in at least four money-management firms around the country. By late afternoon on Feb. 26, U.S. stock markets had fallen close to 300 points from their high the previous week.

Tepper was one of the first prominent money managers to signal concern over COVID-19 in the United States.

On CNBC on Feb. 3, Tepper described the virus as a possible “game changer,” saying that investors needed to be “cautious” until more was known about its reach.

Three weeks later, Callanan’s readout seemed to validate Tepper’s warning.

“I just left D.C. and wanted to reply to your question ASAP,” Callanan wrote to Tepper and one of his senior lieutenants in an e-mail on Feb. 25. “If you can keep the comments below confidential, I would be grateful.”

From there, Callanan reported that numerous Trump administration officials expressed a greater degree of alarm about the coronavirus than the administration was saying publicly.

In a statement, Callanan said his e-mail to Tepper contained “personal and professional views based on extensive research and publicly available information,” showing his “concern on the global pandemic that was emerging.” The e-mail was shared with others without his knowledge or consent, he said.

Tepper initially denied receiving Callanan’s message, then acknowledged in a later interview that he most likely received the e-mail but that it was not memorable.

On Feb. 24, the White House asked lawmakers for $2.5 billion in additional funding. That afternoon, the Hoover group held a panel discussion with members of the Council of Economic Advisers. That talk struck some audience members as worrying for the economy, according to Callanan’s memo and interviews with three people who were there. Of particular note, one of the people said, was the reluctance of Philipson, the council’s acting chair, to estimate the potential effect of the virus on American economic growth for the year, given that the situation was still unfolding.

Philipson confirmed that he had conveyed a message to that effect, though he could not recall specifics.

On Feb. 25, Dr. Nancy Messonnier, a top official from the CDC, gave the first public glimpse of internal government assessments about the potential spread of the virus.

“It’s not so much a question of if this will happen anymore, but rather more a question of exactly when this will happen,” she said.

Shortly after, Kudlow made his “airtight” comments on CNBC. Two hours after that, however, his Hoover presentation struck Callanan as backpedaling.

Kudlow “revised his statement about the virus being contained,” Callanan wrote to Tepper, saying “we just don’t know” whether it was at the time — even as Kudlow continued to downplay its consequences to the private audience. Kudlow “did add that he has recommended to the president a period of ‘tariff tranquillity,’ as markets don’t need more uncertainty now.”

Kudlow confirmed making both assertions, adding that in his mind, they were essentially the same as his remarks on CNBC. “There was never any intent on my part to misinform,” he said.

The Hoover Institution has close relations with the Trump administration, and the White House has pulled from its ranks to fill top positions. Joshua D. Rauh, one of the White House economists addressing the Hoover crowd on Feb. 24, has returned to the institution, where he worked previously. Kevin Hassett, who moderated the panel and has served as the chairman of the White House Council of Economic Advisers, is now a Hoover Institution fellow.