SAN FRANCISCO — More than 10,000 people in the United States are expected to get a flu shot, and that number could rise dramatically as the number of cases continues to drop, a top federal health official said Tuesday.

U.S. health officials are recommending that more than 6 million Americans get a shot, a total of about 15 million people, in the coming months.

A total of 7,000 additional people have been vaccinated in the past month, including those in California and Florida.

The increase in flu shots could be more significant because the virus is already circulating in the air, the official said, and people are already getting more flu shots than they need.

In California, more than 1.1 million people have received shots, but the number could go as high as 2.1, according to the state health department.

California has about 2.5 million people in nursing homes and is expecting to have about 1.3 million by the end of March, which is when the federal vaccine schedule ends, said Dr. Scott Poulsen, California’s health commissioner.

Poulsen said that would put the state well ahead of New York, which has a higher number of people in hospitals and nursing homes.

“We’re not even in the ballpark,” he said.

“We’re getting more people now in our nursing homes than we were a year ago.”

The California government is spending $3.4 billion to vaccinate about 14 million people.

It is also sending more than 2,500 doctors and nurses to help patients get flu shots.