The swine flu outbreak in New York may have spread beyond one school in Queens — where victims now are estimated to number in the hundreds — to pockets across the city, including at least two other schools, officials said on Tuesday.

At Public School 177, a school for autistic children in Fresh Meadows, Queens, 12 students had fever or other symptoms that could indicate swine flu. The school, at 56-37 188th Street, which was closed as a precaution, is about half a mile from St. Francis Preparatory School, at 61-00 Francis Lewis Boulevard, where the first cases were detected several days ago. Tests of students there have not been completed.

About half a dozen children at Ascension School, a Roman Catholic school on 108th Street near Broadway in Manhattan, have come down with fever. That school was not closed, but health officials will test students for swine flu on Wednesday.

Mayor Michael R. Bloomberg said at a news conference that two people had been hospitalized with suspected swine flu — a young boy just admitted to a hospital in the Bronx, and a woman treated on Sunday at a hospital in Brooklyn. Both had family members who had traveled to Mexico, he said.

There were also unconfirmed reports of cases at Ernst and Young, an accounting firm in Times Square, and at Teachers College at Columbia University.

Though the symptoms of the virus in the New York cases have been mild so far, Mr. Bloomberg and Dr. Thomas R. Frieden, the city health commissioner, raised the possibility for the first time on Tuesday that people in the United States could die from the spreading outbreak, even as they urged New Yorkers to keep calm.

“It is here, and it is spreading,” Dr. Frieden said.

The big puzzle, Dr. Frieden said, is why the symptoms of those who have fallen ill so far in New York are mild, and whether the virus will just fizzle or get worse over time, becoming more like the outbreak in Mexico.

By Tuesday, 45 cases of swine flu had been confirmed in New York State, all of which were linked to St. Francis students or their parents, siblings, teachers and friends. An additional 32 cases from around the state are suspected of being swine flu. Officials believe that the flu spread rapidly through the 2,700-member student body at St. Francis, infecting hundreds of other students.

Although a group of students recently returned from a spring-break trip to Cancun, Mexico, officials have not been able to pinpoint where the school’s outbreak began.

The city will not attempt to test all the sick students there, Dr. Frieden said, because it is devoting its efforts now to keeping up with the spread of the disease and containing it.

Mr. Bloomberg noted that even in a normal flu season, 1,000 to 2,000 New Yorkers. typically children or elderly or ill people, die from other strains of the flu, and said that if the swine flu continued to spread, “we may sadly see people either in New York City or nationally” die of it.

Dr. Frieden said officials were aggressively searching out new cases, calling hospitals, doctors and pharmacies, and relying on the city’s sophisticated electronic early warning system, called syndromic surveillance, which relies on detecting patterns of disease.

Mr. Bloomberg and Dr. Frieden urged people to stay calm, taking precautions like washing their hands frequently, but said there was no need to stock up on drugs like Tamiflu.

In the last two days, about 2,000 people have called the city’s information hotline, 311, for advice, and many pharmacies in Queens, where the virus began, had run out of Tamiflu.

Mr. Bloomberg warned against taking Tamiflu unnecessarily, because the virus could become resistant to it over time, and the health department advised people with mild flu symptoms to take Tylenol and drink plenty of fluids.

“Please don’t take it, it may be needed by somebody who’s quite ill,” Dr. Frieden said. The manufacturer, he said, had assured the city that “there is plenty in the supply chain” if it is needed.

St. Francis, where an alert school nurse first informed the health department that dozens of students were mysteriously falling ill last Thursday, will be closed for the rest of the week. An announcement on the school Web site said that SAT tests scheduled for this Saturday had been postponed.

At Teachers College, the president, Susan Fuhrman, alerted students Tuesday to a classmate who got a diagnosis Sunday of Type A influenza, which has been linked to swine flu.

An employee outside the Ernst and Young building in Times Square said workers had been informed by voice mail and e-mail messages as early as Monday morning that one employee had swine flu. They were told that she had gone home sick on Friday, and that the building had been decontaminated over the weekend.

But on Tuesday afternoon, employees said they received another voice mail message saying that the case had not been confirmed as swine flu.

At Public School 177, 82 of 380 students called in sick, officials said, though it was not clear how many had flu symptoms and how many were kept home as a precaution.