New Zealand's number of cases rose to 14 Wednesday, including one person not among a school group who recently returned from Mexico.
Officials say the swine flu strain infecting the students is the same as that in Mexico. All were responding well to treatment with antiviral drugs and in voluntary quarantine at home.
New Zealand has 44 other possible cases, with tests under way.
Mexico was taking drastic measures to fight the outbreak. It closed all archaeological sites Tuesday and allowed restaurants in the capital to only serve take-out food in an aggressive bid to stop gatherings where the virus can spread. Schools remained closed until at least May 6.
A regional Beach Soccer championship in Mexico was postponed and all Mexican first-division football games this weekend will be played behind closed doors.
Other countries have reacted by avoiding Mexico. While the U.S., the European Union, and other countries have discouraged nonessential travel to Mexico, Cuba banned flights to and from Mexico and Argentina suspended flights arriving from Mexico.
Cruise lines are avoiding Mexican ports and holiday tour groups are canceling holiday charter flights there.
In Australia, officials were testing more than 100 people with flu symptoms for the virus. It has been ruled out in at least 10 cases.
Health Minister Nicola Roxon told Australian Broadcasting Corp. radio Wednesday that the government had granted health authorities wider powers to contain contagious diseases as a precaution.
Those powers ranged from "using disinfectants on planes or at ports through to the far more extreme ... making sure that people are isolated and perhaps detained if they don't cooperate and are showing symptoms of this disease," she said.
The World Health Organization has raised its alert level to 4 — out of a possible 6 — but has not called for travel restrictions or border closures.
No cases of the disease have been confirmed in Asia, where governments were rushing to try to hold back the virus from the continent and taking strict precautions with travelers at airports.