WHO Assistant Director General Keiji Fukuda said countries should now focus on mitigating the effects of the virus.
The WHO has raised its alert level from three to four, two steps short of declaring a full pandemic.
Mexico earlier said it believed 149 people had now died from the swine flu, though only 20 cases are confirmed.
The US, Canada, Spain and Britain have confirmed milder versions.
'Not inevitable'
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.
Level four means the virus is showing a sustained ability to pass from human to human, and is able to cause community-level outbreaks.
"What this can really be interpreted as is a significant step towards pandemic influenza. But also, it is a phase that says we are not there yet," Mr Fukuda said.
"In other words, at this time we think we have taken a step in that direction, but a pandemic is not considered inevitable."
He said the virus had become too widespread to make containment a feasible option, and said countries must focus on trying to put measures in place to protect the population.
He also stressed that the experts did not recommend closing borders or restricting travel. "With the virus being widespread... closing borders or restricting travel really has very little effects in stopping the movement of this virus," he said.
The first batches of a swine flu vaccine could be ready between four to six months, but it will take several more months to produce large quantities of it, Mr Fukuda said.
Health experts say the virus comes from the same strain that causes seasonal outbreaks in humans. But they say this newly-detected version contains genetic material from versions of flu which usually affect pigs and birds.
Mexico deaths
Earlier, Mexico's Health Minister Jose Angel Cordova said the suspected death toll from swine flu had now risen from just over 100 to 149. Of that number, 20 have been confirmed as swine flu.
All of those who had died were aged between 20 and 50, he said. Infections among young healthy adults was a characteristic of past pandemics.
"We're in the decisive moment of the crisis, the number [of deaths] will continue rising," Mr Codova told a news conference.
He said the first suspected case of swine flu occurred in the southern state of Oaxaca.
He said nearly 2,000 people had been hospitalised since the first case of swine flu was reported on 13 April, but half had now been allowed home.
Schools nationwide are to remain closed until 6 May as the country attempts to grapple with the outbreak.
In almost all swine flu cases outside Mexico, people have been only mildly ill and have made a full recovery.
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