The death toll from an outbreak of a human swine flu virus has risen to more than 80 in Mexico as new suspected cases have been reported as far apart as Auckland in New Zealand and New York in the United States.

The World Health Organisation said at least 81 people had died from severe pneumonia caused by the flu-like illness in Mexico. It said the virus has pandemic potential but it has stopped short of issuing a worldwide alert, while it gathers more information.

The New Zealand government announced today it was "likely" that ten students have who had recently returned from Mexico have contracted the virus.

Twenty-five students and teachers in New Zealand, some with flu-like symptoms, were quarantined and tested for swine flu after returning from a trip to Mexico. The group, from New Zealand's largest high school, returned to the northern city of Auckland yesterday on a flight from Los Angeles.

Eight students at a school in the Queens area of New York are "likely" to have contracted the virus, according to the New York Times.

In London, tests showed that a member of cabin crew on a British Airways flight from Mexico City did not have swine flu. The man, who has not been named, was taken to hospital yesterday with "flu-like symptoms" after landing at Heathrow.

A hospital spokesman said: "I can confirm he does not have swine flu. All the tests have come back negative."

The UK Health Protection Agency said it was keeping a close eye on the situation involving human cases of swine influenza in case of any threat to people in this country.

An HPA spokesman said: "No cases of swine flu have been identified in the UK or anywhere in Europe."

Mexican authorities ordered the closure of schools in the capital and the states of Mexico and San Luis Potosi until 6 May. Soldiers and health workers patrolled airports and bus stations, looking for people showing symptoms, which include a fever of more than 100 degrees and coughing.

Twenty people are known to have died in Mexico so far out of a total of 1,324 reported cases, and 48 more deaths are thought to be attributable to the outbreak.

At least nine swine flu cases have been reported in California and Texas. The most recently reported California case, the seventh there, was a 35-year-old woman who was treated in hospital but recovered. The woman, whose illness began in early April, had no known contact with the other cases. At least two more cases have been confirmed in Kansas.

State health officials said yesterday they had confirmed swine flu in a married couple living in the central part of the state after the husband visited Mexico. They have not been hospitalised, and the state described their illnesses as mild. Dr Jason Eberhart-Phillips, Kansas's state health officer, said: "Fortunately, the man and woman understand the gravity of the situation and are very willing to isolate themselves."

The Mexican government yesterday authorised President Felipe Calderón to invoke powers allowing the country's health department to isolate patients and inspect homes, travellers and baggage. Mexico's health secretary, José Angel Córdova, said: "We are very, very concerned."

Yesterday, people in Mexico City were being ordered not to kiss or shake hands. Football matches went ahead without spectators, theatres, shops and museums were closed, staff were inside locked schools scrubbing classrooms with disinfectant, and health workers patrolled buses, ordering sickly looking people home.

Scientists have long feared that a new flu virus could launch a worldwide pandemic. Evolving when different flu viruses infect a pig, a person or a bird, mingling their genetic material, a hybrid could spread quickly because humans would have no natural defences.

The director general of the WHO said: "We are seeing a range of severity of the disease, from mild to severe, and of course death. The eight cases in the US have been mild in terms of severity and it is too premature to calculate the mortality rate of this disease."

Any doubts over the extent of the emergency were dispelled last night by the sight of soldiers handing out blue surgical masks to pedestrians and motorists along Mexico City's central boulevard, Paseo de la Reforma. With TV and radio calling on the population to seek medical advice for any flu-like symptoms, queues grew at clinics and hospitals across the city.

Calderón said his government learned only on Thursday night what kind of virus Mexico was facing after tests by specialist laboratories in Canada confirmed the outbreak as a type - labelled A/H1N1 - not previously seen in pigs or humans. Few of the cases appear to have had any contact with live pigs.

The WHO said the virus appeared to be able to spread from human to human and contained human virus, avian virus and pig viruses from North America, Europe and Asia.

Given how quickly flu can spread, there might be cases incubating around the world already, said Dr Michael Osterholm at the University of Minnesota: "Hundreds and thousands of travellers come in and out [of Mexico] every day."

It was unclear how much protection current vaccines might offer. A "seed stock" genetically matched to the new virus has already been created by the US Centres for Disease Control. If the US government decides vaccine production is necessary, it would be used by manufacturers to get started.

At Mexico City's international airport, passengers were questioned to try to prevent anyone with flu symptoms from boarding aircraft and spreading the disease. The Foreign Office issued a warning to UK travellers about the outbreak, but stopped short of recommending people did not visit Mexico. US health officials took a similar line, urging visitors to wash their hands frequently.