One adult and one child have been hospitalized in New York and the city's confirmed swine flu cases could be much higher than the 45 as reported by the Centers for Disease Control and Prevention (CDC), Mayor Michael Bloomberg said on Tuesday.

Both hospitalized patients, a two-year-old Bronx boy and a woman in Brooklyn with suspected swine flu, are now recovering, the mayor said.

So far, all the confirmed cases are from St. Francis Preparatory School in Fresh Meadows, Queens, though authorities are probing P.S. 177, a public school not far away from St. Francis, and Ascension School in Manhattan for possible cases.

Bloomberg warned that the number of confirmed cases in St. Francis Preparatory School could go much higher if all the more than 100 students with flu-like symptoms were tested.

"We can get a lot more by just testing everybody at St. Francis," the mayor told a press conference. "You'll be shocked if out of the other 100 plus students who have a cough and a fever don't have it."

So far, the majority of the cases are all very mild and need no hospitalization.

Bloomberg said authorities have decided to stop testing each and every one of them because "it does not add any new information."

"If they are very sick, we'll test every case in the city," he said. "If they are just mild, we're just going to focus on other things."

Bloomberg said there are five new probable cases in New York City, with two unrelated to the St. Francis private school.

Eleven students at P.S. 177, a special needs school that is also known as the Robin Sue Ward School for Exceptional Children, were sent to hospital Monday after complaining of high fever. Three adults, including the school's assistant principal, were also sent home.

The assistant principal tested negative for swine flu.

According to the school's guidance counselor, the child of one of the teachers at P.S. 177 is one of the students at St. Francis Preparatory School who is confirmed to have swine flu.

Aside from St. Francis, which remained closed on Tuesday, and P.S.177, where students were sent home with a letter saying the school would be closed on Wednesday, most of the city's schools remained open.

In flyers taken home by students, the city's Department of Health and Mental Hygiene urged parents to be "alert but calm."

There were no evident signs of panic in New York, though some of the city's drug stores have run out of face masks and hand sanitizers, as was the case at a Rite Aid on Northern Boulevard at85th Street in Queens.

Monica Granja, the 27-year-old manager, said the items had been bought up as early as Monday morning.

"I just hope it doesn't get close to us," said Granja, who has a 7-year-old son.

At a CVS drugstore several blocks away, customers are asked to check back Thursday evening or Friday morning.

On the chain's website, CVS.com, all face masks are listed as "out of stock" Tuesday afternoon, even the one with a warning that "it does not eliminate the risk of contracting any disease or infection," which was available the night before.

In Atlanta, CDC acting director Richard Besser said the total of confirmed swine flu cases has risen to 64, with at least five having been hospitalized -- three in California and two in Texas.

"I fully expect we will see deaths from this infection," Besser said.

In addition to the 45 in New York, the other confirmed cases are 10 in California, six in Texas, two in Kansas and one in Ohio.

"We are in a pre-pandemic period," Besser said.

In neighboring Mexico, the epicenter of the current outbreak, swine flu was believed to have killed 149 people and hospitalized 776 others. Another 1,070 people were treated for the flu, but were well enough to go home.