Cuba suspended flights to and from Mexico on Tuesday, becoming the first country to impose a travel ban, as the fast-moving swine flu strain extended its reach overseas and in the United States. World health officials in Geneva said they believed the virus appeared to be establishing itself in communities and could produce larger outbreaks outside Mexico. In the US, there were new reports of hospitalizations among those affected, and officials are watching for a potential flu pandemic. "It's a very serious possibility, but it is still too early to say that this is inevitable," the World Health Organization's flu chief, Dr. Keiji Fukuda, told a telephone news conference. The global health body insisted that travel restrictions were ineffective, but Cuba's 48-hour suspension came as the EU's disease control agency as well as Canada, Israel and France warned against nonessential travel to Mexico. "Border controls do not work. Travel restrictions do not work," WHO spokesman Gregory Hartl said, recalling the 2003 SARS epidemic that killed 774 people, mostly in Asia, and slowed the global economy. "There was much more economic disruption caused by these measures than there was public health benefit," he said, adding that WHO is advising countries to provide treatment for the sick and make sure national plans are in place to ease the effects of a larger outbreak. Mexico City closed gyms, swimming pools and pool halls on Tuesday, and ordered restaurants to limit service to takeout - extending a growing shutdown that already included schools, movie theaters and other public places. But the swine flu has already spread to at least six countries besides Mexico, prompting WHO to raise its alert level on Monday but not call for travel bans or border closings. WHO raised the alert level to Phase 4, meaning there is sustained human-to-human transmission causing outbreaks in at least one country. WHO's pandemic alert system was revised after bird flu in Asia began to spread in 2004. Monday was the first time it has ever been raised above Phase 3. Fukuda cited a New York City case in which some students were infected with the virus, but did not travel like some of their infected classmates to Mexico, where most of the people confirmed with the virus were stricken. He said health experts are examining the situation. WHO calls this "community transmission" and says it's a key test for gauging whether the spread of the virus has reached pandemic proportions. In the US, federal health officials said Tuesday that the number of confirmed cases rose to 64, and states say there were at least four more. The Los Angeles County coroner's office told the Los Angeles Times the recent deaths of two men were being examined for links to swine flu. Flu deaths are nothing new in the United States or elsewhere. The Atlanta-based Centers for Disease Control and Prevention estimates that about 36,000 people died of flu-related causes each year, on average, during the 1990s in the United States. But the new flu strain is a combination of pig, bird and human viruses that humans may have no natural immunity to. New Zealand reported that 11 people who recently returned from Mexico contracted the virus. Tests conducted at a WHO laboratory in Australia confirmed three cases of swine flu among 11 members of the group who were showing symptoms, New Zealand Health Minister Tony Ryall said. Officials decided that was evidence enough to assume the whole group was infected, he said. Israel's Health Ministry confirmed two swine flu cases in men who recently returned from Mexico. One has recovered and the other was not believed to be in serious danger, health officials said. Meanwhile, a second case was confirmed Tuesday in Spain, Health Minister Trinidad Jimenez said, a day after the country reported its first case. The 23-year-old student, one of 26 patients under observation, was not in serious condition, Jimenez said. With the virus spreading, the US stepped up checks of people entering the country and warned Americans to avoid nonessential travel to Mexico. "We anticipate that there will be confirmed cases in more states as we go through the coming days," Homeland Security Secretary Janet Napolitano said on NBC's "Today" show on Tuesday. The Food and Drug Administration late Monday issued emergency guidance that allows certain antiviral drugs to be used in a broader range of the population in case mass dosing is needed to deal with an outbreak. Mexico, where the number of deaths believed caused by swine flu rose on Monday to 152, is suspected to be the center of the outbreak. But Mexican Health Secretary Jose Angel Cordova late Monday said no one knows where the outbreak began, and implied it may have started in the US "I think it is very risky to say, or want to say, what the point of origin or dissemination of it is, given that there had already been cases reported in southern California and Texas," Cordova told a press conference. Mexico City Health Secretary Armando Ahued said three people died in the capital Monday, but it was unclear if they were included in the national toll. He said 6,610 people went to city hospitals Monday with flu symptoms, but only 29 were remained hospitalized. Dr. Nancy Cox of the CDC has said she believes the earliest onset of swine flu in the US was on March 28. Cordova said a sample taken from a 4-year-old boy in Mexico's Veracruz state in early April tested positive for swine flu. However, it is not known when the boy, who later recovered, became infected. A decision by WHO to put an alert at Phases 4 or 5 signals that the virus is becoming increasingly adept at spreading among humans. Phase 6 is for a full-blown pandemic, characterized by outbreaks in at least two regions of the world. Symptoms include a fever of more than 100, coughing, joint aches, severe headache and, in some cases, vomiting and diarrhea. Many victims have been in their 30s and 40s - not the very old or young who typically succumb to the flu. So far, no deaths from the new virus have been reported outside Mexico. It could take four to six months before the first batch of vaccines are available, WHO said. Some antiflu drugs do work once someone is sick. The best way to keep the disease from spreading, the CDC's acting director, Richard Besser, said, is by taking everyday precautions such as frequent handwashing, covering up coughs and sneezes, and staying away from work or school if not feeling well. Russia, Hong Kong and Taiwan said they would quarantine visitors showing symptoms of the virus. World stock markets fell Tuesday as investors worried that any swine flu pandemic could derail a global economic recovery. In the US, stocks fell moderately in early trading as investors worried that a growth in swine flu cases could hurt industries such as travel and tourism.