WASHINGTON — Top health officials in the United States and abroad yesterday projected a cautious optimism that the new virus is not as lethal as initially feared.

Genetic analysis has failed to detect in the influenza virus the "virulence factors" seen in the killer 1918 Spanish flu or the bird flu that surfaced earlier this decade, said Richard Besser, acting director of the U.S. Centers for Disease Control and Prevention.

Moreover, the new virus may have been more widespread in Mexico than originally reported, which would make the seemingly high mortality rate there a misperception, he added.

"We are starting to see that there was widespread flu in Mexico," Besser said on NBC's "Meet the Press," as he joined two other Obama administration officials in making the rounds of talk shows. "As we learn more about how widespread this is, it may be that the rates of severe disease in Mexico will end up being not different than what we see here."

In Mexico, Health Secretary Jose Angel Cordova said that the outbreak is "in its declining phase" there as hospitals report fewer new and serious cases.

Still, Cordova warned, "We can't let down our guard," and the situation remains shot through with unknowns.

It took on a new twist with reports this weekend from the Canadian province of Alberta that a farmworker who recently had returned from Mexico had apparently passed the virus to a herd of pigs. The farmworker and the pigs have recovered, and the World Health Organization said there is no sign that the virus mutated or adapted into a more virulent form.

Health officials took pains to say that there is no danger of infection from eating pork that is properly cooked. A food safety scientist at the World Health Organization, Peter Ben Embarek, said cured pork products are safe because of their long maturation process. "You can continue to safely eat your prosciutto," he said.

U.S. Agriculture Secretary Tom Vilsack said in a statement that there is no evidence of the new virus in American pigs, and he noted that the Canadian herd had been quarantined. He added, "As a precaution, people with flulike symptoms should not interact with swine."

This is a delicate moment for U.S. public health officials, who are dealing with a skittish public, a rapidly moving virus and lingering memories of the Bush administration's botched response to Hurricane Katrina. The officials want to relay the encouraging news of recent days and hours without exposing themselves to ridicule in the event the virus shifts into a different gear and causes a devastating pandemic.

The new virus is one for which most people probably have limited immunity (though the CDC noted that it does not seem to be showing up very often in Americans older than 50, suggesting that they possess some immunity to it). The virus has also appeared after the end of the normal flu season. The latest tally shows that the virus is in 35 states.

Across the country, there have been instances of what some have called overreaction. The entire school district in Fort Worth, Texas, closed after a single case of swine flu. Emergency rooms reportedly have been swamped by people complaining of a cough. Administration officials said healthy people should still go to graduation events, ride public transportation and so on. "Common sense: You don't need to wear a mask," Homeland Security Secretary Janet Napolitano said on "Fox News Sunday."

Public health officials have advised schools to close for up to 14 days if they have one or more cases of the swine flu, but there has been no similar advice to businesses.

"We don't want to shut down the production capacity of the country for a flu when that's not necessary," Napolitano said on ABC's "This Week."