Speaking in Geneva, an expert from the World Health Organization (WHO), the UN's health agency, expert said the swine flu virus could be capable of mutating into a more dangerous strain but that more information was needed before raising the WHO's pandemic alert phase.
Only a handful of the Mexican cases have so far been laboratory-confirmed as swine flu, while in the US confirmed cases had only mild symptoms.
Health experts want to know why some people become so seriously ill, while others just get a bit of a cold, the BBC's Imogen Foulkes reports from Switzerland.
The WHO added that there was no evidence to suggest the outbreak was a bio-terrorist attack.
It 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.
Swine flu is a respiratory disease found in pigs
Human cases usually occur in those who have contact with pigs
Human-to-human transmission is rare and such cases are closely monitored
Officials said most of those killed so far in Mexico were young adults - rather than more vulnerable children and the elderly.
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.
WHO experts will meet again in Geneva on Tuesday to discuss whether to raise the pandemic alert phase.
H1N1 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.
It is spread mainly through coughs and sneezes.
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
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.
Suspected cases have been detected beyond Mexico, the US and Canada
Ten New Zealand students from a group which visited Mexico have tested positive for Influenza A, making it "likely" they are infected with swine flu
In France, a top health official told Le Parisien newspaper there were unconfirmed suspicions that two individuals who had just returned from Mexico might 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
Two people in Queensland, Australia, are being tested in hospital after developing flu-like symptoms on returning from Mexico
The BBC's Ros Atkins dons his face mask to explore Mexico City
Officials in Mexico confirmed that 20 people had died from the virus while another 83 deaths were suspected cases of swine flu.
More than 1,300 people have been admitted to hospital with suspected symptoms since 13 April.
With Mexico City apparently the centre of infection, many people are choosing to leave the city, the BBC's Stephen Gibbs reports.
Schools, universities and even most bars and restaurants will remain closed for several days and though Sunday church services are going ahead, priests have been asked to place Communion wafers in people's hands rather than on their tongues.
There are those that are beginning to worry about the effects swine flu is having on their livelihoods and the Mexican economy in general, our correspondent says.
Not knowing exactly how the virus works and how it can be killed off creates a horrible uncertainty
Fear of the virus is expected to persuade many tourists to cancel their holidays and Mexican exports are already beginning to be affected.
The World Bank is providing Mexico with more than $200m in loans to help it deal with the outbreak.
Russia has banned imports of raw pork and pork products from Mexico and the US states of California, Texas and Kansas until further notice as a precaution.
Dr Fukuda said on Sunday there was no proof that eating pork would lead to infection.
"Right now we have no evidence to suggest that people are getting exposed, or getting infected, from exposure to pork or to pigs, and so right now we have zero evidence to suspect that exposure to meat leads to infections," he said.
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