But officials say they need more information on the virus to determine the threat it poses.
Dr Keiji Fukuda, WHO's assistant director-general in charge of health security, said all countries were "looking at this situation very seriously".
"But it's also clear that we are in a period in which the picture is evolving... [and that] we have to be very careful to collect the best possible information," he said.
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.
Most of those who have died so far in Mexico were young adults.
The H1N1 virus is the same strain that causes seasonal flu outbreaks in humans but the newly detected version contains genetic material from versions of flu which usually affect pigs and birds.
There is currently no vaccine for the new strain, but severe cases can be treated with antiviral medication. Dr Fukuda said years of preparing for bird flu had boosted world stocks of anti-virals.
In the US, eight cases have been confirmed among New York students, seven in California, two in Texas, two in Kansas and one in Ohio.
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
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
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
"I do fear that we will have deaths," Dr Anne Schuchat of the US Centers for Disease Control and Prevention (CDC) told reporters.
The Canadian cases were recorded at opposite ends of the country: two in British Columbia in the west, and four in the Atlantic province of Nova Scotia.
In Spain, a young man who had recently returned from Mexico was found to have the virus. He was said to be in a stable condition.
A number of countries in Asia, Latin America and Europe have begun screening airport passengers for symptoms.
Russia, China and Thailand have banned imports of raw pork and pork products from Mexico and parts of the US. But Dr Fukuda said that there was no evidence to link exposure to pork with infection.
In the Mexican capital, schools, bars and public buildings remain closed and many people are choosing to stay indoors.
Some people are beginning to worry about the effects swine flu is having on their livelihoods and the Mexican economy in general.
Fear of the virus is expected to lead to many tourists cancelling their holidays and Mexican exports are already beginning to be affected.
Mexico: 103 dead - 20 confirmed to have died from swine flu, 18 confirmed ill with swine flu
United States: 20 confirmed cases of swine flu
Canada: 6 confirmed cases
Spain: 1 confirmed case, 17 others being investigated
UK, Israel, Brazil, Australia and New Zealand: suspected cases being tested. Suspected cases in France tested negative
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