He also urged local public-health bodies to be vigilant and said schools with confirmed cases "should consider closing".
Texas Governor Rick Perry said closing the US border with Mexico was an option, but added that taking that step now would be "a little premature".
The assistant director general of the World Health Organization (WHO), Keiji Fukuda, said that although the virus originated in pigs, it was now being transmitted from human to human.
"It is clear that the virus is spreading and we don't see evidence of it slowing down," he told reporters from WHO headquarters in Geneva.
He added that moving the pandemic alert to five - the second highest - from the current four would be a significant step, but was not necessary at the moment.
He said the WHO would do so if infected people in at least two countries were spreading the disease to other people in a sustained way.
The WHO has said measures like travel bans were unlikely to prove effective.
France will ask the European Union on Thursday to suspend all flights going to Mexico because of the flu outbreak, Health Minister Roselyne Bachelot said.
From Matthew Price in Oaxaca, Mexico
At the local cemetery, a group of gravediggers pointed me towards a freshly dug plot. The flowers on top had wilted under the sun but still had some colour. Here was the grave of the first confirmed victim of the virus, Adela Gutierrez, 39.
One of the gravediggers, Sergio Castro Lopez, told me people here are worried. They are waiting for the authorities to tell them what they should do.
In Spain, the government said the first person to contract swine flu without having travelled to Mexico was the boyfriend of a young woman who had recently returned from there.
Spanish Health Minister Trinidad Jimenez said such cases were to be expected.
In total, the number of confirmed cased in Spain rose from two to 10 on Wednesday. None of them are seriously ill.
In Mexico, the search for the source of the outbreak continues, with the focus on the vicinity of a pig farm in the eastern part of the country.
The Mexican government is urging against jumping to conclusions and is suggesting the possibility remains that the virus originated outside the country.
Schools across Mexico have closed, public gatherings are restricted and archaeological sites have been placed off-limits.
Mexico City's chamber of commerce estimated restrictions in the city were costing businesses there at least 777 million pesos ($57m or £39m) a day.
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