WASHINGTON — As he announced on Friday that booster shots would be available to some Americans, President Biden made a prediction: His administration was likely to soon provide third doses of the vaccine “across the board” to anyone who wanted one.

“In the near term, we’re probably going to open this up,” he told reporters in remarks from the State Dining Room at the White House.

But that assessment — a politically popular one in a country where most people vaccinated against the coronavirus say they are eager for a booster — was the latest example of how Mr. Biden and some of his team have been ahead of the nation’s top public health scientists, who have emphatically said in recent days that there is simply not enough evidence to suggest that boosters are necessary for the entire American population.

In fact, two panels of scientists — one for the Food and Drug Administration and the other for the Centers for Disease Control and Prevention — voted in recent days against recommending boosters for everyone after fierce public debates streamed online.

The president’s Friday remarks were the second time in two months that he had suggested boosters would be available to everyone. And they were issued on the same day that Dr. Rochelle P. Walensky, the C.D.C. director and one of the president’s political appointees, came under fire for allowing boosters for a broader group of people than her agency’s own immunization panel recommended.

Taken together, the announcements by Mr. Biden and Dr. Walensky did not sit well with all of the scientists who advise them, raising questions about the president’s pledge to always “follow the science” as he fought the pandemic. While some of them credited the C.D.C. director for charting a course through uncertain waters, others warned that politics had intruded on scientific decisions — something that Mr. Biden had promised to avoid after the blatant pressures seen during the Trump administration.

“Everybody uses this statement ‘follow the science’ very glibly, and I think that the science here did not warrant picking out a group of people and saying that you may be at more risk for acquiring an infection,” said Dr. Sarah S. Long, a member of the C.D.C.’s advisory committee, referring to the groups of workers who were made eligible for booster shots.

Dr. Long, who is a professor of pediatrics at Drexel University College of Medicine, said that a president telegraphing his opinion before the formal public health process undermined the expert advisers, calling it a violation of the “checks and balances” built into the system. She also criticized Dr. Walensky for expanding the number of people eligible for the boosters.

If that pattern of reversals were to extend beyond boosters, she said, that “would be the end of the vaccine program as you know it.”

But a number of other committee members — including some who also resisted a broad expansion of the booster program — defended Dr. Walensky’s ruling, adding that federal regulators authorized additional shots less than 24 hours before the C.D.C.’s advisers were asked to give guidance. That left them little time to hammer out the language of their recommendations, much less to debate the type of issues that were weighing on Dr. Walensky, like staffing needs at hospitals or schools.

“During a time when we have over 2,000 Americans dying per day, we’re not in a position to sit on our hands and wait,” said Dr. Camille Kotton, the clinical director of transplant and immunocompromised host infectious diseases at Massachusetts General Hospital. “We need to act as quickly and thoughtfully as we can.”

Still, the C.D.C.’s medical advisers largely said on Friday that fresh attempts from the White House to get ahead of parts of the booster campaign undercut the sort of clarity that the public desperately needed.

“I hope, despite the pandemic being a public health emergency, that we would have the space and the grace to be able to continue to use our process,” said Dr. Grace Lee, the immunization committee’s chairwoman and a professor of pediatrics at Stanford University School of Medicine.

For the president to be subject to that kind of criticism is exactly where he promised he would never be.

As a candidate, Mr. Biden repeatedly denounced President Donald J. Trump for pressuring scientists at the C.D.C. and the F.D.A. In March, after becoming president, Mr. Biden repeated what officials have said is his North Star on the pandemic during a visit to the C.D.C.’s headquarters in Atlanta.

“There’s an entire generation coming up that is learning from what you’ve done,” he told employees there that day. “I don’t just mean learning about how to deal with a virus. Learning about it makes a difference to tell the truth, to follow the science, and just wherever it takes you, and just be honest about it.”

White House officials insist that the president is doing just that, and they dismiss criticism that his comments about the additional doses amount to undue pressure on the government’s public health experts. They say that the discussion about boosters was initiated by the government’s top doctors and that he made it clear from the beginning that any decision by the administration would be subject to independent review and approval.

And Mr. Biden has deferred far more to the public health experts than did Mr. Trump, who publicly and privately pushed F.D.A. and C.D.C. officials to act more quickly to approve vaccines and actively promoted unproven treatments for the coronavirus like hydroxychloroquine. The former president also clashed repeatedly with scientists about wearing masks and decisions about when to reopen schools, churches and other activities.

But Mr. Biden’s public embrace of booster shots has rankled many in the public health sector, including those working inside the government, who say it could have the effect of putting undue pressure on scientists to make a recommendation they do not believe is supported by the evidence.

Some public health officials and doctors say they fear Mr. Biden — who has staked his presidency on successfully managing the pandemic — is pushing for boosters because they are politically popular. A Reuters/Ipsos national survey conducted Aug. 27-30 found that 76 percent of Americans who have received at least one shot of a vaccine want a booster. Only 6 percent do not, the poll found.

In mid-August, the president told the nation that his administration planned to deliver booster shots to everyone starting the week of Sept. 20, pending decisions by the F.D.A. and the C.D.C.

“Just remember as a simple rule, eight months after your second shot, get a booster shot,” he said during remarks at the White House.

That turned out to be premature. Only Pfizer, one vaccine maker, has won authorization to administer additional doses, and for just some of its recipients.

On Wednesday, the F.D.A. authorized boosters, but only for older adults, people with underlying health conditions and some frontline workers who are frequently exposed to the virus.

The agency’s decision stood in direct contrast to Mr. Biden’s earlier comments.

Doctors were also split on Friday over the decision by Dr. Walensky to overrule her own panel of immunization experts.

On Thursday, the panel voted to recommend boosters for older adults and those with underlying health issues. But it advised against allowing frontline workers like teachers and nurses who have already been vaccinated to get a booster shot.

In a decision announced early Friday morning, Dr. Walensky rejected that last recommendation and said that the C.D.C. would allow the frontline workers to receive boosters. In a briefing for reporters later on Friday, she defended the move, noting that the panel was sharply divided on the issue.

“Our teachers are facing uncertainty as they walk into the classroom, and I must do what I can to preserve the health across our nation,” Dr. Walensky said, calling it “a first step” and saying that “we will continue to review new data on effectiveness and experience with the third shot, as it becomes available.”

Dr. Steven Joffe, a professor of medical ethics and health policy at the University of Pennsylvania, said that with such a close vote at the C.D.C.’s meeting, it was reasonable for Dr. Walensky to rule a different way. But he suggested that she could have been influenced by the support she and the administration had earlier shown for a broader distribution of the booster.

“To what extent did she feel like she was bound to follow that line of decision-making?” he said. “I can’t get inside her head and answer that question. The fact that the final decision makers had already staked out their final positions had put the advisory committees in a very difficult position.”

Jason L. Schwartz, an associate professor of health policy at the Yale School of Public Health, said that Dr. Walensky’s intervention “reflects just how closely and directly engaged the senior political appointees are in shaping this booster program.”

He predicted her involvement was “going to color” the expert committee’s future work.

Michael D. Shear reported from Washington, and Benjamin Mueller from New York. Noah Weiland contributed reporting from Washington.