Health officials had been giving priority to certain groups, including pregnant women, health care workers and those between the ages of 4 and 24. Clinics also had been vaccinating adults with underlying medical conditions - such as asthma, diabetes, heart and lung conditions, or a weakened immune system - that can make the flu even more dangerous.
"It's simpler; everybody can get it who wants it," said Nassau's health commissioner, Dr. Maria Torroella Carney.
New York got only about 23 percent of its anticipated supply of the H1N1 virus vaccine in October, the first month it became available.
The state is now getting weekly vaccine shipments that are double the volume of earlier allocations.
So far, New York has received more than 5 million vaccine doses, including more than 3 million doses for areas outside New York City.
Health officials said the flu is still widespread across the state and they encouraged taking advantage of the change in policy.
"While the flu is very unpredictable, typically we see the most flu activity during the next three months," said Dr. Richard Daines, state Health Department commissioner. "Getting vaccinated in the next month will provide protection against a possible third wave of the H1N1 flu this winter and spring."
Dr. Aaron Glatt, chief executive of New Island Hospital in Bethpage and a spokesman for the Infectious Diseases Society of America, echoed Daines. "This is a real window of opportunity."
Both county health commissioners welcomed not having to give the vaccine only to those in priority groups and said there was now plenty of vaccine.
Carney especially encouraged those 65 and older to get the shot, pointing out that about a quarter of all deaths since September from H1N1 have been older people.
Suffolk's acting health commissioner, Dr. Linda Mermelstein, said the department has been getting calls from doctors who have gotten their own shipment of H1N1 vaccine along with some from the county and wanted to return the excess.
"We are at the point we want to get it out to everyone," she said. She said those on a waiting list for the vaccine are being contacted to set up appointments.
Finding seasonal flu vaccine, however, remains harder, Glatt said - although he said there has been little sign of seasonal flu so far. He said people should check with their doctors about its availability. "There may be a little more coming," he said.
With Ridgely Ochs