The development suggests the disease is now being passed among people who had never left the US.
In other US developments on Tuesday Barack Obama, the US president, has asked congress for $1.5bn to fight the outbreak to build drug stockpiles and monitor future cases.
Arnold Schwarzenegger, governor of the US state of California where at least 13 cases have been confirmed, has declared a state of emergency to tackle the crisis.
And in Cuba authorities have barred flights to and from Mexico for 48 hours in a bid to prevent the spread of swine flu to the country.
The WHO says 26 deaths in Mexico have been confirmed to be from the disease.
Mexican authorities have put the nation’s capital on high alert, ordered restaurants to serve only takeaway food and closed schools until May.
Franc Contreras, Al Jazeera’s correspondent in Mexico City, said: “People are feeling confusion because of different flu figures coming from the federal government on the one hand, and the city government on the other.
“And if you listen to government figures, they say the number of cases are also beginning to level off.
“But health officials across Mexico will tell you they’re swamped and that their own teams have begun to get sick now.”
In addition, the US Centres for Disease Control and Prevention on Tuesday raised the number of cases in the US to 64, saying the new count includes a number of “hospitalisations”.
One other case was reported in the US state of Indiana.
Others have been confirmed in Canada, Israel, the UK, New Zealand and Spain, while there are also suspected cases in South Korea, Brazil, Guatemala, Peru and Australia.
Authorities and health experts say it is still not clear why deaths have only occurred in Mexico.
The WHO said on Tuesday that it was not recommending travel restrictions or border closures to fight the spread of swine flu, despite more nations confirming cases of the virus.
The US government has already declared a public health emergency and is advising against non-essential travel to Mexico where the outbreak started.
Gregory Hartl, a WHO spokesman, said in Geneva on Tuesday: “Border controls don’t work. Screening doesn’t work.”
He said infected people may not show symptoms at the airport or when they reach a border crossing.
Travel limitations such as those imposed during the Sars (Severe Acute Respiratory Syndrome) outbreak in 2003, which killed nearly 800 people, Hartl said, were therefore ineffective.
|Swine flu: At a glance|
Countries with confirmed cases: Mexico, the US, Canada, New Zealand, Spain, Israel and Britain
Countries with suspected cases: Australia, Brazil, France, Chile, Denmark, Switzerland, Austria, Colombia, Germany, Norway, South Korea, Guatemala
“Certainly if you feel that you are ill, you should not travel, in any case, to anywhere,” he said.
However, Androulla Vassiliou, the European Union’s health chief, said on Tuesday: “I don’t see any point of restricting travelling.”
She had said on Monday she was personally in favour of avoiding non-essential travel to affected areas.
The WHO also confirmed on Tuesday that transmission of the virus was human-to-human and not from animal or other contact.
“There is no danger form eating pork,” Hartl said. “If you cook pork well, if you cook all meat well, it kills all virus.”
The WHO’s emergency committee decided not to meet later on Tuesday to review the pandemic alert level, which was raised on Monday evening to level four from three, on a one-to-six scale.
“If the virus is an efficient virus, if it spreads easily from human to human, it will probably continue to spread,” Hartl, the WHO spokesman, said.
“We are still at phase four because we do not have incontrovertible evidence this is an efficient spreader.”
Trying to allay fears of a pandemic on Monday, Ban Ki-moon, the UN secretary-general, said: “We don’t know yet which way it will go, but we are concerned that in Mexico most of those who died were young and healthy adults.”
High fatality rates
Most of the swine flu fatalities were aged between 20 and 50. A hallmark of past pandemics has been the high rate of fatalities among young adults.
Richard Fielding, a clinical psychologist in public health at the University of Hong Kong, told Al Jazeera: “Concern is warranted at this stage but panic is not.
“The media have a role. One sees it [swine flu] described as a ‘deadly influenza epidemic’. I think balanced reporting is important.”
Worldwide, seasonal flu kills between 250,000 and 500,000 people in an average year. The new strain is worrying as it spreads rapidly between humans and there is no vaccine for it.