About a third of the confirmed U.S. cases of swine flu are people who had been to Mexico and likely picked up the infection there, a federal health official said Saturday.

But investigations indicate many cases are getting the illness here, and that it probably still is spreading, said Dr. Anne Schuchat of the U.S. Centers for Disease Control and Prevention.

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In a press briefing, CDC officials said the agency knows of confirmed cases from 30 states.

The swine flu cases range in age from 1 to 81, but the majority are people younger than 20, said Schuchat, the CDC's interim deputy director for science and public health. Most U.S. cases have been relatively mild; only 13 have been hospitalized.

President Obama is working with Mexico's president on ways to keep the swine flu from spreading further and says the U.S. will be ready if the flu strain develops into something worse.

Obama and Mexican President Felipe Calderon spoke for 20 minutes Saturday to share information about each country's efforts and the importance of close U.S.-Mexican cooperation, the White House said.

Meanwhile, Mexico reported three new deaths from the swine flu epidemic Saturday and urged citizens not to let their guard down against a virus that has killed 19 in people in Mexico and is spreading across Asia and Europe.

Health Secretary Jose Angel Cordova said Mexico's confirmed swine flu cases jumped to 473, including the 19 deaths. The previous death toll in Mexico was 16. A Mexican toddler also died in Texas days ago, for a worldwide total of 20.

Mexico's last confirmed swine flu death occurred Wednesday, Cordova said. However, he said there were 11 cases of people suspected to have died from the virus in the last 24 hours. The alarming news came after the epidemic's toll in Mexico appeared to be leveling off.

Cases outside Mexico suggested the new swine flu strain is weaker than feared, but governments moved quickly anyway to ban flights and prepare quarantine plans. Experts warned the virus could mutate and come back with a vengeance.