Fourteen countries have reported confirmed cases of the H1N1 strain, with France, the Netherlands, Denmark and Hong Kong the latest to join the list.
At least 17 other countries, including Ireland, are checking possible cases. Normal seasonal flu kills between 250,000 and 500,000 people around the globe in an average year, including about 36,000 in the United States.
The largest number of confirmed cases outside Mexico is in the United States, with 141. Almost all infections outside Mexico have been mild, and only a handful of patients have required hospital treatment.
Mexico has reported 176 deaths from the new strain of the H1N1 virus. Only one person has died outside Mexico, a Mexican toddler who died in Texas.
Mexico started a five-day shutdown of most offices and businesses today to try to halt the spread of the strain, and officials said they were encouraged by signs that the number of new cases was falling.
Health minister Jose Angel Cordova said the public hospitals that treat roughly half the country admitted just 46 patients with severe flu symptoms yesterday, down from 212 patients on April 20th. "This is encouraging," he said.
The World Health Organisation says experts do not yet know enough about the new strain to say how deadly it is, how far it might spread and how long any potential pandemic may last.
It said today that no meeting of its emergency committee was scheduled, meaning there was no immediate likelihood of its level 5 alert being raised to a full phase 6 pandemic alert. To declare a full-blown pandemic, WHO would have to be convinced the new virus is spreading in a sustained way among communities in another region besides North America.
Today, a WHO vaccine expert said there was no doubt that it would be possible to make a successful vaccine against the virus in a reasonably short period.
The United States has 141 confirmed cases of the H1N1 flu in 19 states, the CDC said today, an increase from 109 in 11 states yesterday. President Barack Obama said he was confident in the US government's ability to handle the flu outbreak and said that officials were planning ahead for the long term.
Mr Obama told reporters after a Cabinet meeting today that he was pleased with the progress so far in dealing with the public health emergency and said he was "optimistic we're going to be able to manage this effectively."
Although Spain has had one case of a traveller from Mexico infecting someone else, WHO spokesman Thomas Abraham said that "we need to be sure it is actually established in communities, not just stray cases of a traveller passing it on to one person or two people".
Germany also reported that a nurse there had caught the virus from treating a man who had recently come from Mexico.
Two people in France are infected with the H1N1 flu, health ,inister Roselyne Bachelot said tonight, confirming the country's first cases of the new virus.
The WHO said yesterday it would call the new virus strain Influenza A (H1N1), not "swine flu", to appease outraged meat producers, since there is no evidence that pigs have the virus or can transmit it to humans.
Both Roche AG's Tamiflu, known generically as oseltamivir, and GlaxoSmithKline's Relenza, known as zanamivir, have been shown to work against the new virus.
The United States has begun sending 400,000 doses of treatment to Mexico. But Greece, which has not reported any cases of the new virus yet, banned the export of Relenza and Tamiflu.
Mexican president Felipe Calderon has asked Mexicans to stay home from May 1st to 5th over the long Cinco de Mayo holiday, and urged businesses to close. The streets of the capital were much quieter than usual.
"There is no safer place than your own home to avoid being infected with the flu virus," Mr Calderon said.
Measuring the spread of the new flu has been difficult because of the lack of diagnostic facilities in Mexico. Of Mexico's 176 presumed H1N1 deaths, only around a dozen have been confirmed, at laboratories in the United States or Canada. Almost a third of the bodies were buried before proper tests could be carried out.
But a lab equipped with kits specifically designed to test quickly for the new strain has now been set up in Mexico, the US Centres for Disease Control and Prevention (CDC) said.