Pfizer and BioNTech said on Tuesday that they had sought emergency authorization for a second booster shot of their coronaviruses vaccine for adults 65 and older.

The companies requested the FDA to approve their shots based on data from Israel. Their move could further inflame a debate among scientists over when and how the vaccines should be strengthened.

Over the past week, Pfizer's chief executive, Dr. Albert Bourla, said he believed an additional dose was necessary to counteract waning protection after the third dose.

He told CBS that the third is good enough for hospitalizations and deaths.

There was a fierce public debate over previous requests for a booster shot. Some public health experts were against a third dose for the general population only to change their minds after the Omicron variant was able to evade the vaccines.

Scientists are at odds over how long the vaccines last and how much benefit added shots offer. A fourth dose could be more controversial than a third.

In an interview with Business Insider on Monday, the president of Moderna sounded a bit more cautious than Dr. Bourla.

For those who are immune-compromised, those who are older adults, over the age of 50 or at least 65, we want to strongly recommend and encourage a fourth shot. He said that most people would need an annual coronaviruses shot just like the flu shot.

Pfizer and BioNTech cited two recent studies from Israel in their justification. A study done in conjunction with Israel's Ministry of Health found that people who got a fourth dose of Pfizer's vaccine were less likely to get the disease.

Since Israel only recently began its second booster program, researchers couldn't determine if the added protection would last. Israel began giving fourth doses to health care workers in late December, and quickly expanded their eligibility to include people over the age of 60.

The second study, of Israeli health care workers, showed that the fourth shot of either Pfizer or Moderna's vaccine was not very effective in preventing infections. Researchers said the findings underscored the need for vaccines that target whatever variant is circulating.

Various vaccine manufacturers and the National Institutes of Health in the United States have been studying how the vaccines could be updated. A federal health official said the results wouldn't be expected until the summer.

Senior administration officials say that a second booster is not a good idea for the general population. The issue of fourth shots is expected to be discussed by the F.D.A.'s expert advisory committee next month. The Washington Post reported on developments on Pfizer's request.

Dr. Peter Marks, the F.D.A.'s top vaccine regulator, was asked last month if everyone would need another injection.

About two-thirds of Americans 5 and older have been fully protected from vaccine-related diseases. According to the Centers for Disease Control and Prevention, only half of those eligible for boosters have received them, but the proportion increases to two-thirds for those 65 and older.

In a call with reporters on Tuesday, senior administration officials said the administration was short on funds for new doses. One person said the administration has enough supply to manage a fourth shot for people 65 and older, but could not expand it to everyone without more funding from Congress.

The C.D.C recommends that Americans with immune deficiencies get three shots as part of their initial series, followed by a fourth shot as a booster. A big question mark hangs over everyone else.

A study released by the agency last month showed waning protection after a booster shot. Researchers did not break down cases by age, underlying conditions or the presence of immune deficiencies, but they said the findings showed the importance of a fourth shot.

The study looked at hospitalizations and visits to emergency rooms and urgent care clinics by people who received booster shots of either Moderna or Pfizer-BioNTech. The level of protection against hospitalization fell from 91 percent in the two months after a third shot to 78 percent after four to five months. The effectiveness against emergency room and urgent care visits decreased.

According to Pfizer and BioNTech, the effectiveness of a booster dose against both symptom and disease fades in three to six months, while a fourth dose restores the peak level triggered by a third dose.

A recent study suggests that three or even two Covid vaccine doses are enough to protect most people from serious illness and death for a long period of time. According to at least four studies published in top-tier journals, the immune system can remember and destroy the virus over a long period of time.

E. John Wherry, the director of the Institute for Immunology at the University of Pennsylvania, said in an interview last month that the number of additional doses is diminishing.