In addition, eight suspected cases are being investigated at a New York City high school where about 200 students fell mildly ill with flu-like symptoms
Ten New Zealand students are among a group which travelled to Mexico have tested positive for influenza A - making it "likely", though not definite, that they are infected with swine flu, said Health Minister Tony Ryall
In France, a top health official told Le Parisien newspaper there were unconfirmed suspicions that two individuals who had just returned from Mexico may be carrying the virus
Spain's health ministry says three people who returned from a trip from Mexico with flu symptoms are in isolation and being tested
In Israel, medics are testing a 26-year-old man who has been taken to hospital with flu-like symptoms after returning from a trip to Mexico
But a UK hospital conducting tests for swine flu on a British Airways cabin crew member said the tests proved negative.
The Mexican government, which has faced criticism for what some see as a slow reaction to this outbreak, is now taking an increasingly hard line to try to contain the virus, says the BBC's Stephen Gibbs in Mexico City.
Public buildings have been closed and hundreds of public events suspended.
There is a sense of chaos in hospitals and we do not know what to do
Schools in and around Mexico City have been closed until 6 May, and some 70% of bars and restaurants in the capital have been temporarily closed.
People are being strongly urged to avoid shaking hands, and the US embassy has advised visitors to the country to keep at least six feet (1.8m) from other people.
Mexico's Health Secretary, Jose Cordova, said a total of 1,324 people had been admitted to hospital with suspected symptoms since 13 April and were being tested for the virus.
"In that same period, 81 deaths were recorded probably linked to the virus but only in 20 cases we have the laboratory tests to confirm it," he said.
Mexico's President Felipe Calderon has announced emergency measures to deal with the situation.
They include powers to isolate individuals suspected of having the virus without fear of legal repercussions.
In Mexico, face masks are handed out, while the head of the WHO voices concern
In the US, seven people in California, two people in Texas, and two people in Kansas have been infected with the new strain.
In New York, city health commissioner Dr Thomas Frieden said preliminary tests conducted on the ailing students showed they were possible cases of swine flu.
Further tests will clarify if it was the same strain that was detected in the other three states.
Following a meeting of its emergency committee on Saturday, the WHO said the virus had the potential to become a pandemic but it was too early to say whether that would happen.
1918: The Spanish flu pandemic remains the most devastating outbreak of modern times - infecting up to 40% of the world's population and killing more than 50m people, with young adults particularly badly affected
1957: Asian flu killed two million people. Caused by a human form of the virus, H2N2, combining with a mutated strain found in wild ducks. The elderly were particularly vulnerable
1968: An outbreak first detected in Hong Kong, and caused by a strain known as H3N2, killed up to one million people globally, with those over 65 most likely to die
WHO Director General Margaret Chan said recent events constituted "a public health emergency of international concern" and that countries needed to co-operate in heightening surveillance.
The WHO is advising all countries to be vigilant for seasonally unusual flu or pneumonia-like symptoms among their populations - particularly among young healthy adults, a characteristic of past pandemics.
Officials said most of those killed so far in Mexico were young adults - rather than more vulnerable children and the elderly.
There is currently no vaccine for the new strain but severe cases can be treated with antiviral medication.
It is unclear how effective currently available flu vaccines would be at offering protection against the new strain, as it is genetically distinct from other flu strains.
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