NEW YORK — The nation is facing a severe shortage of seasonal flu and H1N1 vaccines, a situation that many federal and independent health officials agree was unavoidable because the global swine flu pandemic has heightened demand for all flu immunizations well beyond the production capabilities of vaccine manufacturers.

But many of those officials also concur that the shortage does not mean that there will be an increase in seasonal flu deaths, which average about 36,000 a year. They say there is no reason to believe that any of the three strains of seasonal flu will be worse this winter.

Still, in New York City, the shortage of vaccines has been so acute that the city’s health department has appealed to physicians to suspend administering seasonal flu immunizations to healthy adults under age 65. And shortages of the vaccines have been reported across the country.

Concerns grew when President Obama declared the spread of the H1N1 virus a national emergency, a move that gives hospitals more leeway in the strategies they select to cope with a potential surge of flu-related patients, including the possibility of establishing off-site facilities to increase the number of beds for new flu patients as well as to protect patients already hospitalized but not infected with the flu.

The Centers for Disease Control and Prevention estimates that up to 85 million Americans have already received seasonal flu immunizations, compared with only about 61 million who had been vaccinated at this time a year earlier.

According to a number of experts, the current problems began years ago when vaccine companies began abandoning the American market. Vaccines, which involve living viruses, are more difficult to manufacture than most drugs. Profits for the vaccines declined, unused flu vaccines expired after a few months and lawsuits increased, particularly in cases in which vaccine use allegedly had harmed children.

It wasn’t until bioterrorism concerns emerged after the 2001 anthrax attacks, followed two years later by fears over the H5N1 avian flu virus, that manufacturers began reentering the U.S. market.

As recently as five years ago, only two companies were licensed to sell flu vaccine in the United States. Currently, there are five such manufacturers, but only one of the companies — Sanofi-Pasteur Inc. — maintains a domestic plant.

The other manufacturers — Glaxo­SmithKline PLC, Novartis AG, CSL Ltd. and Medimmune Inc. — rely on foreign facilities.

Despite rising concerns over the vaccination shortage, Health and Human Services Secretary Kathleen Sebelius noted last month that the H1N1 vaccine “is coming out the door’’ as quickly as it leaves production lines.

“We were relying on the manufacturers to give us their numbers, and as soon as we got numbers we put them out to the public,” Sebelius said. “It does appear now that those numbers were overly rosy.”