South Korean officials have found a suspected case of swine flu in a woman who recently returned from Mexico.
New Zealand has confirmed the first cases of swine flu in the country - also thought to be the first in the Asia-Pacific region.
Health authorities are carrying out clinical tests on the woman, officials and news reports said.
Health Minister Tony Ryall told reporters that at least three students who had recently returned from Mexico had tested positive for the disease.
Mexico, with 149 deaths suspected to be due to the virus, is the epicentre. The World Health Organization (WHO) has raised its alert level.
Other nations in the region are testing travellers to check for symptoms.
In Asia, several countries have been conducting tests on travellers to check for symptoms of swine flu.
In Australia, 19 people are being tested for the virus and several hundred others are being sought.
In Australia, 19 people are being tested, with several hundred more who might have had contact with the disease being sought.
China is on full alert, as several children have fallen ill with symptoms resembling those of swine flu.
New Zealand has identified 10 probable cases, and is investigating another 56 among people who have recently returned from Mexico or neighbouring countries.
In South Korea, a woman who recently returned from Mexico is undergoing clinical tests.
China and Thailand are among the countries reported to have banned imports of meat products from some parts of the US and Mexico as they attempt to protect themselves from the virus.
China and Thailand are among the countries reported to have banned imports of meat products from some parts of the United States and Mexico as they attempt to protect themselves, although experts say there is no evidence to link exposure to pork with infection.
Human to human
More than 150 people are already thought to have died from the disease in Mexico, and cases have also been confirmed in the US, Canada and Europe.
The South Korean case involves a 51-year-old Korean woman who has been quarantined at her home near the capital, Seoul, and given antiviral medicine, said Jun Byong-yul of the Korea Centers for Disease Control and Prevention.
The World Health Organization has warned that swine flu has "pandemic" potential, but it has yet to reach this stage.
She had returned home from Mexico via Los Angeles on Sunday, he said.
School infection
Two other people in South Korea who were suspected to have contracted the virus have tested negative.
"Unfortunately tonight we can confirm New Zealanders have tested positive to swine flu," Health Minister Tony Ryall told reporters.
Asian countries have stepped up checks at airports
The WHO's decision to raise the alert level to four came after an emergency meeting of experts, brought forward by a day because of concerns over the outbreak.
The 11 people concerned - 10 students and one teacher - are from an Auckland secondary school, and had come down with flu-like symptoms after returning from a three-week visit to Mexico.
The level was raised from three to four - two steps short of declaring a full pandemic.
Mr Ryall said a World Health Organization laboratory in Australia had tested three samples from the 11 people and confirmed they had the H1N1 swine flu strain. The other eight samples were also assumed to be positive.
Level four means the virus is showing a sustained ability to pass from human to human, and is able to cause community-level outbreaks.
New Zealand is also monitoring a further 43 people for possible signs of swine flu.
WHO Assistant Director General Dr Keiji Fukuda said a pandemic was not inevitable, but containment was no longer plausible and countries should focus on protecting the population.
Hong Kong, Australia, Japan, New Zealand, Taiwan, South Korea and Singapore have all advised against non-essential travel to Mexico.
In Mexico 149 people are believed to have died from the swine flu outbreak, though just 20 cases there are confirmed.
Stock markets around the region have fallen due to investor fears that an outbreak could derail economic recovery.
Other, milder, cases are confirmed in the US, Canada, Spain and Britain.
Vaccine
Earlier, Beijing banned pork imports from Mexico and the US states of Texas, Kansas and California with immediate effect, according to state news agency Xinhua.
FLU PANDEMICS 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 affected1957: 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 vulnerable1968: 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
China's Ministry of Health has warned its citizens to be vigilant, although it also noted that so far there is no evidence that the new flu virus can be spread through food.
Thailand was also reported to have banned meat and pork imports from some parts of the US.
In Hong Kong, where the Severe Acute Respiratory Syndrome (Sars) killed hundreds of people in 2003, a series of tough measures have been announced.
All travellers are to be screened on arrival and anyone who is ill will be quarantined.
Japan, Singapore, Malaysia and Indonesia have announced similar plans, with many airports using devices that were put in place to monitor Sars and bird flu over the last few years.
Tokyo has announced that Mexican citizens will no longer be able to obtain visas on arrival in Japan.
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.
Mr Fukuda of the WHO said the first batches of a swine flu vaccine could be ready in four to six months, but it would take several more months to produce it large quantities.
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