The White House recently received a sobering warning about the potential for the coronavirus to come roaring back, with experts reaching a consensus that there’s a roughly 20 percent chance during the next two years of an outbreak rivaling the onslaught of illness inflicted by the Omicron variant.

A forecast from one widely regarded scientist pegged the risk at a more alarming level, suggesting a 40 percent chance of an Omicron-like wave.

White House officials spoke with about a dozen leading experts in virology, immunobiology, and other fields about the prospect that the virus would again develop mutations that allow it to evade protections from vaccines and treatments. Those discussions, not previously reported, came as the administration plans for the May 11 end of the public health emergency that was declared at the dawn of the pandemic.

Some experts based their conclusions on existing research, and at least one, computational biologist Trevor Bedford of the Fred Hutchinson Cancer Center in Seattle, conducted new statistical analysis about the potential for a coronavirus wave.

“No one’s saying it’s zero. No one’s saying it’s 80 percent,’’ said Dan Barouch, an immunologist and virologist at Harvard Medical School, who spoke with the White House. “It’s more than an infinitesimal chance — and it is by no means a certainty.’’

The experts’ analysis was shared in a report among Biden administration leaders this spring, as they weighed how to wind down their coronavirus response team and set up initiatives intended to provide longer-term pandemic protections. Several of those initiatives — including a next-generation vaccine program and a program to cover coronavirus vaccines and COVID treatments for the uninsured — are at risk as Republicans seek to claw back unspent coronavirus funds as part of ongoing debt ceiling talks in Congress.

The White House declined to comment about the experts’ analysis.

“The administration has conversations with a broad range of experts, both inside and outside of government, on a number of issues,’’ a White House spokesperson said in an e-mail.

Senior officials have publicly emphasized the need to implement more public health protections to guard against the next viral threat, even as political will and funding fades along with the threat from the coronavirus.

“One of my biggest worries is that we are losing time in preparing for the next pandemic,’’ Dawn O’Connell, assistant secretary for preparedness and response at the Department of Health and Human Services, told a Senate committee Thursday.

Rochelle Walensky, the Centers for Disease Control and Prevention director who announced Friday that she was stepping down, also warned the Senate panel that her agency still faces challenges such as limitations on collecting data from hospitals and local health departments about potential outbreaks.

“We can’t act swiftly, nimbly, robustly if we can’t see what is happening from a data standpoint,’’ Walensky said.

The World Health Organization on Friday declared that the pandemic is no longer a global health emergency, but WHO director General Tedros Adhanom Ghebreyesus cautioned that the announcement “does not mean that COVID-19 is over as a global health threat.’’

Confirmed COVID cases and deaths have plunged in recent months, with public health experts crediting the immunity conferred by vaccines and prior infections for curbing the virus’s risks.

Fewer than 80,000 confirmed coronavirus cases were reported across the United States last week — the lowest figure since March 2020. But the actual rate of infection is almost certainly far higher than the reported numbers, with many Americans testing at home, if at all, and opting not to report their results.

The potential for large indoor gatherings to fuel coronavirus infections remains high, as illustrated by about three dozen cases linked to a CDC conference last week. The virus remains on pace to be one of the top 10 causes of death this year, with fatalities concentrated among older and immunocompromised individuals.

“What most people don’t understand … this virus isn’t going away,’’ said Eric Topol, director of the Scripps Research Translational Institute, who also spoke with the White House about its projections.

Most of the infections in the United States since December 2021 have been caused by Omicron and its subvariants, raising the prospect that a new strain of the virus — with a set of novel mutations — could surprise immune systems conditioned to fight Omicron.

Bedford said he believes there is about a “40 percent chance of an Omicron-like event between today and May 2025,’’ he wrote in an e-mail to The Washington Post this week, citing the analysis he shared with the White House and the logic that there had been one Omicron-level event so far during the pandemic, which began in early 2020.

Bedford said he understood why the WHO and the United States were ending their public health emergencies but added that the world is entering a stage of the COVID response that will pose new challenges.

“Even if the pandemic is over, endemic COVID is still going to be a major public health concern,’’ he said.