Initial reports from the WHO said that up to 60 people had died in Mexico from the disease, and Cordova said 40 deaths were being "analysed" for the disease.
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.
Al Jazeera's Franc Contreras in Mexico City said the authorities had advised people not to go outside unless necessary and that many residents had bought surgical masks in attempt to avoid the disease.
The WHO, which has identified swine influenza as a potential source of a human flu pandemic, 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 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.