Mexicans are being advised to stay at home during the shutdown
Mexico has revised down the suspected death toll from swine flu from 176 to 101, indicating that the outbreak may not be as bad as was initially feared.
Health Minister Jose Angel Cordova told the BBC that, based on samples tested, the mortality rate was comparable with that of seasonal flu.
Mexico has ordered a five-day shutdown in a bid to contain the virus.
A World Health Organization official said there was no evidence of sustained virus spread outside North America.
WHO Director of Global Alert and Response Dr Michael Ryan said the emergence of more cases in Europe did not mean the WHO would necessarily need to raise its global pandemic alert level.
"I think it would be, at this stage, unwise to suggest that, in any way, those events are out of control or spreading in an uncontrolled fashion," he told a daily press briefing.
"I think the next few days will tell as this develops."
Mexico: 101 suspected deaths - 16 confirmed
US: One death, at least 141 confirmed cases
New Zealand: 4 confirmed, 12 probable cases
Canada: 35 confirmed cases
UK, Spain: 15 confirmed cases
Germany: 4 confirmed cases
France, Israel, Costa Rica: 2 confirmed cases
Netherlands, Switzerland, Austria, Denmark, Hong Kong, South Korea, Italy: 1 confirmed case
Countries with confirmed cases of secondary transmission
The WHO is sending 2.4m courses of antiviral treatment to 72 nations around the world, Dr Ryan said, among them many developing countries.
The WHO was still trying to establish the severity of the swine flu virus, he added.
Italy reported its first case on Saturday, bringing the number of countries affected to 17.
In Egypt, authorities have begun in earnest the slaughter of more than 300,000 pigs, in what was originally described as a precaution against swine flu.
Officials now say the move is a general health measure aimed at restoring order to Egypt's pig-rearing industry.
Experts say the virus cannot be caught from eating pork and there is no scientific rationale for the cull.
Five countries outside Mexico have confirmed person-to-person transmission.
China is trying to stop the spread of the virus, after getting its first case on Friday.
It says it will quarantine all those who travelled on a flight from Mexico with a man suffering from swine flu.
Flights from Mexico have been suspended, and fellow guests and staff at the Hong Kong hotel where he was staying have been quarantined.
South Korea has also now confirmed a case of the virus.
In cases outside Mexico, the effects do not appear to be severe.
Dr Anne Schuchat, acting deputy director of America's Centers for Disease Control and Prevention (CDC), said that although experts were concerned about the possibility of severe cases, the majority so far had been "mild, self-limited illness".
The new virus lacked the traits that made the 1918 flu pandemic so deadly, another CDC official said.
Mr Cordova appeared to agree, saying that the Mexican authorities may, on reflection, have overestimated the danger.
He said 43.7% of samples from suspected cases so far tested had come back positive, a total of 397. Sixteen in this group had died.
"All the samples that were taken give us an idea of the percentage of the ones testing positive," he said.
"That means that apparently, the rate of attack is not as wide as was thought."
But he stressed that the risk of a rise in infection remains and some elements of the five-day shutdown might be extended.
Restaurants, public buildings and businesses have been closed as Mexico tries to bring the virus under control, and people are being urged to stay at home.
Mexico City Mayor Marcelo Ebrard said the emergency measures were bringing results, with the numbers "getting better every day".
There is growing concern about the effect the virus could have on Mexico's economy.
Several US air carriers say they will cut flights to Mexico as demand falls amid concerns over the crisis. Tourism has plummeted since the outbreak was declared a week ago.