Mexico’s flu season is usually over by now, but health officials have noticed a significant spike in flu cases since mid-March. The W.H.O. said there had been 800 cases in Mexico in recent weeks, 60 of them fatal, of a flulike illness that appeared to be more serious than the regular seasonal flu. Mr. Córdova said Friday that there were 1,004 possible cases.

Still, only a small number have been confirmed as cases of the new H1N1 swine flu, according to Gregory Hartl, a W.H.O. spokesman. Mexican authorities confirmed 16 deaths from swine flu and said 45 others were under investigation, most of them in the Mexico City area. The C.D.C. said that eight nonfatal cases had been confirmed in the United States, and that it had sent teams to California and Texas to investigate.

Image People wearing surgical masks at the General Hospital in Mexico City on Friday. Credit... Dario Lopez-Mills/Associated Press

“We are worried,” said Dr. Richard Besser, the acting head of the C.D.C. “We don’t know if this will lead to the next pandemic, but we will be monitoring it and taking it seriously.”

There is no point in trying to use containment measures in the United States, he said, because the swine flu virus has already appeared from San Antonio to San Diego, without any obvious connections among cases. Containment measures usually work only when a disease is confined to a small area, he said.

The C.D.C. refrained from warning people not to visit Mexico. Even so, the outbreak comes at an awful time for tourism officials, who have been struggling to counter the perception that violence has made Mexico unsafe for travelers. The outbreak was also causing alarm among Mexicans, many of whom rushed to buy masks or get checkups.