As Mexico shut schools and museums and axed public events, global health officials stopped short of declaring a pandemic.
But they warned more cases could come to light, making up a major outbreak, as the flu spreads between people and infected some individuals who had no contact with one another.
The World Health Organization said the virus from 12 of the Mexican patients was the same genetically as a new strain of swine flu, designated H1N1, seen in eight people in California and Texas who later recovered.
The Mexican government said the flu had killed 20 people and it may also be responsible for 48 other deaths. In all, 1,004 suspected cases have been reported nationwide.
Health Minister Jose Angel Cordova, speaking on the evening television news, encouraged people to avoid crowds and wear face masks, noting there was no guarantee that going to get a flu vaccine would help against the new strain.
He said the death rate appeared to have steadied and hospitals in the past few days had not seen the exponential rise in the number of people infected that many had feared.
Genetic analysis shows the flu strain is a never-before-seen mixture of swine, human and avian viruses.
The fact most of the dead were aged between 25 and 45 was seen as a worrying sign linked to pandemics, as seasonal flu tends to be more deadly among the elderly and the very young.
"We realize the seriousness of this problem," Mexican President Felipe Calderon told health officials on Friday.
MORE CASES COULD EMERGE
In California, Dr. Gil Chavez, director of the Center for Infectious Diseases at the California Department of Public Health and the state's chief epidemiologist, said many more cases could come to light as patients are tested. "The more we look the more we are likely to find," he said.
In New York City, health officials were investigating what had sickened scores of students who fell ill with flu-like symptoms in a Queens high school on Thursday and Friday. The symptoms were reported as mild and a city health official said he could not speculate about which flu strain was responsible.
The U.S. government said it was taking the situation seriously and monitoring for any new developments.
As far away as Hong Kong -- the epicenter of the 2003 SARS epidemic and especially vigilant to any threat of infectious disease -- the government's Center for Health Protection said it was closely monitoring investigations in the United States and would analyze flu samples in the territory.
Cordova said Mexico had 1 million doses of antiviral medicine, easily enough to treat the cases reported so far.
In Mexico City, a crowded metropolis of 20 million people, soldiers handed out surgical masks and the government warned people to avoid close physical contact and sharing food.
Finnish rock band The Rasmus canceled a Mexico City concert and the Mexican Football Federation said two weekend soccer matches would be played with no spectators present as a precaution.
DVD rental stores said customers poured in to rent movies on Friday night so they could huddle inside for the weekend.
The last flu pandemic was in 1968 when "Hong Kong" flu killed about a million people globally.
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