The move came after the virus spread to at least 11 U.S. states from coast to coast and swept deeper into Europe.
"It really is all of humanity that is under threat during a pandemic," said WHO Director General Margaret Chan. "We do not have all the answers right now but we will get them."
In the United States, President Obama mourned the first U.S. death, a Mexican toddler who had traveled with his family to Texas.
Total American cases surged to nearly 100. But there are far more suspected cases, from a military base in California where 30 Marines are quarantined to the University of Delaware, where four people have fallen ill, reports CBS News correspondent Nancy Cordes.
"Schools with confirmed or suspected cases of H1N1 so that we can be as safe as possible," Mr. Obama said.
In Mexico, where the flu is believed to have originated, officials said Wednesday the disease was confirmed or suspected in 159 deaths and almost 2,500 illnesses. But in Mexico City, officials suggested the outbreak there seemed to be stabilizing, with far fewer deaths being reported.
The WHO says the phase 5 alert means there is sustained human-to-human spread in at least two countries. It also signals that efforts to produce a vaccine will be ramped up.
In Washington, Homeland Security Secretary Janet Napolitano was questioned by senators on whether the U.S. should close its border with Mexico. She repeated the administration's position that questioning of people at borders and ports of entry was sufficient for now, and said closing borders "has not been merited by the facts."
The WHO made it clear earlier in the week that the virus had already spread so far and so fast that border restrictions were ineffective.
Mr. Obama made it clear in his primetime news conference Wednesday that he does not support closing the border. He said health officials aren't recommending the measure and likened it - in his words - to closing the barn door after the horses are out.
Mr. Obama said Americans must maintain great vigilance and respond appropriately to swine flu cases cropping up in their communities. He also said the outbreak was cause for deep concern, but not panic.
Dr. Richard Besser, the acting chief of the Centers for Disease Control, said in Atlanta that there were confirmed cases in 10 states, with 51 in New York, 14 in California and 16 in Texas, where officials said Wednesday they were postponing all public high school athletic and academic competitions until May 11.
Two cases have been confirmed in Kansas, Massachusetts and Michigan, while single cases have been reported in Arizona, Indiana, Nevada and Ohio. State officials in Maine said laboratory tests also had confirmed three cases in that state, although those had not yet been included in the CDC count.
Laboratory testing shows the new virus is treatable by the anti-flu drugs Tamiflu and Relenza, and the first shipments from a federal stockpile arrived Wednesday in New York City and several other locations in the U.S. The government was shipping to states enough medication to treat 11 million people as a precaution.
Federal officials insist they have enough courses of the Tamiflu - roughly 50 million - to weather even a major outbreak, reports Cordes.
"The question is how rapidly and effectively can that Tamiflu actually get into the hands of families that need to take it when they need to take it," Dr. Irwin Redlener of Columbia University told Cordes. For the Tamilflu to be effective, a patient must take it within 48 hours of having flu symptoms.
Meanwhile, Egypt's government , though no swine flu cases have been reported there. Egypt's overwhelmingly Muslim population does not eat pork, but farmers raise some 300,000-350,000 pigs for the Christian minority.
The disease is not spread by eating pork, and farmers were to be allowed to sell the meat from the slaughtered animals.
In fact, officials appeared to go out of their way on Wednesday to not call the strain "swine flu." Mr. Obama called the bug the "H1N1 virus."
"The disease is not a food-borne illness," Rear Adm. Anne Schuchat, CDC's interim science and public health deputy direct, told the Senate Homeland Security Committee.
She said the strain is particularly worrisome because "it's a virus that hasn't been around before. The general population doesn't have immunity from it."
People have various levels of protection against other more common types of flu because they are exposed to it over time, and that protection accumulates. She suggested that some older people might have more resistance to this particular strain than younger people because its traits might resemble outbreaks of decades ago.
Germany became the latest country to report swine flu infections. It reported four cases on Wednesday.
New Zealand's total rose to 14. Britain had earlier reported five cases, Spain four. There were 13 cases in Canada, two in Israel and one in Austria.
Mr. Obama said it is the recommendation of public health officials that authorities at schools with confirmed or suspected cases of swine flu "should strongly consider temporarily closing so that we can be as safe as possible."
He was underscoring advice that the CDC provided earlier to cities and states, and that some schools - most prominently in New York City - already have followed.
"If the situation becomes more serious and we have to take more extensive steps, then parents should also think about contingencies if schools in their areas do temporarily shut down, figuring out and planning what their child care situation would be," Mr. Obama advised.
He advised people to take their own precautions - washing hands, staying home if they are sick, and keeping sick kids home.
Mr. Obama said the federal government is "prepared to do whatever is necessary to control the impact of this virus." He noted his request for $1.5 billion in emergency funding to ensure adequate supplies of vaccines.
CDC for days has said people with flulike symptoms should stay home - but now also is stressing that other family members should consider staying home or at least limiting how much they go out until they're sure they didn't catch it.
Besser, the acting CDC director, called it "an abundance of caution," but stressed that it's voluntary and that the government hasn't urged actual quarantine, which isn't really effective with flu.
Besser told The Early Show that trying to determine why the disease has caused so many more fatalities in Mexico than elsewhere was "a critical question" for American scientists working on the ground with their counterparts south of the border.
Swine Flu News Worldwide: