A third of the world's population could be infected by the H1N1 flu virus in the next year, a top U.N. health official said on Thursday, urging Asian governments to stay alert for a potentially wider pandemic.

Keiji Fukuda, acting assistant director-general for the World Health Organization (WHO), also said it was "quite likely" the WHO would declare a pandemic in the near future but a final decision had not been made.

"This is a disease that could potentially infect a third or more of the world's population in the next several months, in the next year," Fukuda told Asian health officials meeting in Bangkok via a conference call from Geneva.

He added that "even if the illnesses appear relatively mild on a global level, the global population level adds up to enormous numbers".

Health ministers from Japan, China, South Korea and the 10-member Association of South East Asian Nations (ASEAN) will attend the Bangkok meeting on Friday to discuss efforts to coordinate their fight against the virus.

Flu Timeline

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Meanwhile, the virus continues to set off health alarms. A Texas woman with the H1N1 flu virus died early Tuesday after being hospitalized since April 19, state health officials said, the second death outside of Mexico.

Officials identified the woman as a 33-year-old pregnant schoolteacher who fell into a coma and had her baby delivered by Caesarean section. State health department spokeswoman Carrie Williams said Judy Trunnell had "chronic underlying health conditions" but wouldn't give any more details.

U.S. health officials have predicted that the swine flu virus would spread and inevitably kill some people, just as seasonal flu does. Last week a Mexican toddler visiting Texas also died.

On Thursday, Jose Angel Cordova, Mexico's health secretary, said tests confirmed two more deaths from swine flu, bringing the toll to 44.

This brings Mexico's infection tally to 1,160, up 90 from the previous confirmed number of cases. Cordova said at a news conference Thursday that the number of new cases continues to decrease.

The World Health organization also confirmed more infections in Britain, Spain, Italy and Germany — taking the U.N. agency's toll to more than 2,000 officially reported cases in 23 countries.

The bulk of these remain in North America.

The United States has more than 640 confirmed cases, the CDC said, with another 700 "probable" cases. Canada has reported at least 165 cases.

Vaccine in Sight

Health officials told lawmakers Wednesday it took only two weeks to identify the genetic characteristics of swine flu, and they are in good position to quickly produce a vaccine if the flu takes a turn for the worse.

At the same time, the officials cautioned members of a House Foreign Affairs subcommittee that there are still elements of what they called the novel 2009 H1N1 influenza virus that they don't understand, and it was not time for complacency.

"We have isolated and identified the virus and discussions are under way so that, should we need to manufacture a vaccine, we can work towards that goal very quickly," Dr. Anne Schuchat, acting deputy director for science and program at the Centers for Disease Control and Prevention told a U.S. House hearing.

Dr. Dennis Carroll, a special adviser on pandemics with the U.S. Agency for International Development, said investments to stave off an avian flu epidemic helped lay the groundwork for the quick response to swine flu.

The Associated Press and Reuters contributed to this report.