New York Mayor Michael Bloomberg says two people are hospitalized with suspected swine flu.

City Health Commissioner Thomas Frieden also said Tuesday that "many hundreds" of schoolchildren are sick with suspected cases of swine flu.

Bloomberg says the hospitalizations are separate from the outbreak at a private school in Queens.

Bloomberg said that 82 of 380 students at P.S. 177 in Queens, a school for autistic children, have called in sick. A third school in Manhattan is being evaluated because students there are sick, Frieden said.

The mayor says the hospitalized are a child in the Bronx and an adult in Brooklyn.

The U.S. has 68 confirmed cases of swine flu, including 45 in New York City. The sickness has killed dozens in Mexico. Twenty-eight of the 45 New York cases are clustered at St. Francis Preparatory School in Queens — the largest Catholic High School in the country.

“Thanks to the cooperation of students and staff at St. Francis Preperatory School in Fresh Meadow, Queens, we do however have a much firmer grasp now of the situation at that school,” Bloomberg said during a news conference Monday.

“Many family members of these students and staff are also sick," he continued. "We would normally expect to see 1 out of every 5 family members of a person with flu get sick — and that is exactly what we’re seeing with swine flu. And very reassuringly all of the cases have been mild both in students and in staff.”

In New York, the city called on the CDC for additional resources to investigate the outbreak at St. Francis Prep.

Some of the New York students who tested positive for swine flu after a trip to Mexico passed it on to others who had not traveled — a significant fact because it suggests the strain suspected in dozens of deaths in Mexico can also spread through communities in other countries, said Keiji Fukuda, assistant director-general of the World Health Organization.

"There is definitely the possibility that this virus can establish that kind of community wide outbreak capacity in multiple countries, and it's something we're looking for very closely," Fukuda said. So-called "community" transmissions are a key test for gauging whether the spread of the virus has reached pandemic proportions.

Fukuda warned, however, against jumping to the conclusion that the virus has become firmly established in the United States.

Still, U.S. officials stressed there was no need for panic and noted that flu outbreaks are quite common every year. The CDC estimates about 36,000 people in the U.S. died of flu-related causes each year, on average, in the 1990s.

The increase in cases was not surprising. For days, CDC officials said they expected to see more confirmed cases — and more severe illnesses. Health officials nationwide stepped up efforts to look for symptoms, especially among people who had traveled to Mexico.

About 1,500 students replied to surveys sent out by the health department about the outbreak, helping the city get a better sense of how the virus is spreading. Some students have complained of sudden nausea; others dealt with high fever, sore throats, coughs and aches.

Rachel Mele and her mother, Linda, were relieved when the 16-year-old's fever broke Tuesday for the first time in five days. It had been hovering around 101.

The family could finally breathe easy — a relief after a terrifying night Thursday in which Mele's parents bundled her into the car and rushed her to the hospital when they realized she was having trouble breathing.

"I could barely even catch my breath. I've never felt a pain like that before," Mele said. "My throat, it was burning, like, it was the worst burning sensation I ever got before. I couldn't even swallow. I couldn't even let up air. I could barely breathe through my mouth."

The Associated Press contributed to this report.