An emergency committee of the WHO met in Geneva on Saturday to oversee the agency's handling of the outbreak.
Jose Angel Cordova, the health minister of Mexico, said on Friday that the rate of deaths appeared to be slowing and there were no plans to seal the country's borders, although schools, libraries, museums and theatres were closed in a bid to contain the disease.
The mayor of Mexico City has cancelled all public events for 10 days to try to contain the outbreak.
Two of Mexico's main football games, one of them in the capital's giant Aztec Stadium, will be played without spectators on Sunday to avoid large crowds.
In all, 1,004 suspected cases have been reported nationwide.
US public health officials on Thursday said that eight people had been diagnosed with swine flu in the states of California and Texas.
Tests by the WHO on Friday showed the virus from 12 of the Mexican patients was the same genetically as a new strain of swine flu, designated H1N1, seen in the US patients, AFP reported.
US officials said the White House was closely following the outbreak in the United States and Barack Obama, the president, has been informed.
The officials said the virus in the United States was a never-before-seen mixture of viruses typical among pigs, birds and humans.
Armando Ahued, Mexico City's health minister, said a massive vaccination campaign was being launched against the illness.
|Chan has urged countries to increase
vigilance following the outbreak [AFP]
Franc Contreras, reporting for Al Jazeera from Mexico City, said the authorities had advised people not to go outside unless necessary and that many residents had bought surgical masks in an attempt to avoid the disease.
The WHO said it had activated its global epidemic operations centre, which oversees acute public health events in response to the crisis.
The European Centre for Disease Prevention and Control said the A/H1N1 influenza identified in at least two of the recent cases by US counterparts could certainly develop into a pandemic-type virus.
Human outbreaks of H1N1 swine influenza virus were recorded in the US in 1976 and 1988, when two deaths were recorded, and also in 1986, while in 1988 a pregnant woman died after contact with sick pigs, the WHO said.
In recent years the global focus for a possible pandemic has shifted to the H5N1 bird flu virus, which has spread from poultry to humans and killed 257 of the 421 people infected by the virus since 2003.