WHO spokeswoman Fadela Chaib said "unusual end-of-season influenza activity" was noticed in Mexico starting from the end of March.
"To date there have been some 800 suspected cases with flu-like illness, with 57 deaths in the Mexico City area," she said.
Three more deaths and 24 suspected cases were also recorded in San Luis Potosi in central Mexico, she said.
"We're dealing with a new flu virus that constitutes a respiratory epidemic that so far is controllable," Mexican Health Minister Jose Angel Cordova said on Thursday.
The Mexican authorities are currently conducting tests to determine what the virus is. Schools have been closed in affected areas and people urged to avoid large crowds, shaking hands and kissing.
In the US, experts are investigating a new form of swine flu that they say combines pig, bird and human viruses, after seven people fell ill in Texas and California.
"This is the first time that we've seen an avian strain, two swine strains and a human strain," Dave Daigle, a spokesman for the US Center for Disease Control and Prevention (CDC), told AFP.
This has the potential to be, what we call in laboratory medicine a 'slate-wiper' - and just because the epidemic didn't materialize in 1976 is no reason to be complacent and lackadaisical now. Launching that massive inoculation effort back then was without a doubt the right thing to do - and was successfully executed well enough for that effort to be used as a template for how to do it this time out. Once the vaccine is developed, of course.
