NEW YORK — With the number of influenza cases reaching epidemic levels in many parts of the country, drug chains across the nation have been working to keep their stores supplied with flu vaccine to meet the surging demand for vaccinations.

For example, Walgreen Co., CVS/pharmacy and Rite Aid Corp. all reported flu shot shortages at some stores last month. However, the chains said they expected to adjust distribution quickly to address the shortfalls.

“The current high demand is unprecedented for this time of year, and we are making every effort to resupply our pharmacies and clinics with vaccine as needed,” a spokesman for CVS/pharmacy said, noting that the chain has been able to continue vaccinating patients at most of its stores and the MinuteClinic walk-in health centers it ­operates.

Over the past few years chain drug pharmacies have played an increasingly central role in dispensing flu shots. Few pharmacies across the country do not offer at least some form of a vaccination program.

In fact, executives at Walgreens noted that the chain provides more flu vaccines every year than anyone but the federal government.

With this year’s flu season being one of the most severe in recent memory community pharmacies are becoming besieged with requests for flu vaccinations.

Centers for Disease Control and Prevention (CDC) director Tom Frieden said during the agency’s weekly flu activity briefing in mid-January that 24 states and New York City were reporting a high level of influenza-like illness activity, while 16 reported moderate levels of activity. Forty-seven states are reporting widespread geographic influenza activity, up from 41 the week before.

As a result of the flu outbreaks being heavier in certain areas of the country, many chains have begun redirecting vaccines from one region to another.

“When possible, we’re moving our supply around to meet the demand,” a spokesman for Rite Aid said.

Rite Aid was one of a handful of chains across the country that has been able to acquire additional vaccines.

Still, the company and most other community pharmacy chains have been asking patients to check with their local pharmacy before seeking out a flu shot.

“Since this is a very fluid situation, we’re advising customers to call to see if the flu shot is available so that our team can advise them if it is or let them know when their store’s supply will be restocked,” the Rite Aid spokesman noted.

In at least one state community pharmacies’ role in helping to inoculate people has been ­increased.

In New York, where state health officials say there were nearly 20,000 cases of flu reported as of mid-January compared with just 4,400 for all of last season, Gov. Andrew Cuomo issued an executive order on January 11 temporarily suspending a state law that prohibits pharmacists from administering immunizations to people under 18.

“We are experiencing the worst flu season since at least 2009, and influenza activity in New York state is widespread,” Cuomo said when he issued the 30-day suspension of the law.

Meanwhile, other portions of the country have also been hit hard by the flu outbreak, leading pharmacies in those regions to scramble to find enough vaccine.

Safeway Inc., for instance, announced in mid-January that it was shipping an additional 200,000 doses of flu vaccine to its pharmacies, while Supervalu Inc.’s Jewel-Osco chain said it would ship about 7,000 additional doses of the vaccine to 170 of its pharmacies.

The rush to secure a sufficient amount of flu vaccine to keep up with this year’s demand may become easier as the season progresses, thanks to the Food and Drug Administration’s recent decision to approve a new type of vaccine.

The new vaccine, developed by a small company called Protein Sciences, is made with a process that does not require the virus to be grown in chicken eggs, as is now generally done, meaning that it can be produced quickly.

Protein Sciences said it expects to have about 150,000 doses of the new vaccine — called Flublok — available later this winter.