Updated

U.S. health officials say they see "encouraging" signs that the new swine flu may be less severe than some had feared, but warned that Americans still need to take precautions to keep the virus contained.

"We're not out of the woods," Richard Besser, acting director of the Centers for Disease Control and Prevention, told "FOX News Sunday."

Homeland Security Secretary Janet Napolitano, Health Secretary Kathleen Sebelius and Besser hit the Sunday talk show circuit to update the public on the strain and defend what they called the government's "aggressive" approach to fighting the virus.

"This is a rapidly evolving situation. There's a lot of uncertainty," Besser said, noting that too much is better than not enough when it comes to prevention. "We are not overreacting to this outbreak."

But he said that while the H1N1 influenza A virus will have a "significant impact" on Americans' health, the strain so far does not appear to be more severe than the seasonal flu.

Sebelius said the strain that is in the United States has not had the kind of lethal effect it has had south of the border in Mexico.

Around the world, there were mixed signals over the weekend about the extent and severity of the outbreak.

In just a 24-hour period, Mexican officials reported 11 suspected cases where people died from the virus, despite signs the number of people infected was leveling off. The country has reported 506 confirmed cases, including 19 deaths.

The worldwide toll was at about 900, with 228 confirmed cases across 34 states in the United States. Officials said the virus was widespread in the United States.

Authorities say it's spreading just as easily as regular winter flu, but fortunately doesn't seem to cause as severe disease as it did in Mexico. The only other country to record a death from swine flu so far is the United States, where a Mexican toddler died in Texas.

Napolitano on Sunday defended the decision not to close the U.S.-Mexico border.

"We take our lead from science," she said.

The CDC says its own count is outdated almost as soon as it's announced. More cases are being confirmed daily. About one-third so far are people who had been to Mexico and probably picked up the infection there. Many newly infected people are getting the illness in the U.S., and the CDC says it probably still is spreading.

If the new flu proves no more lethal than regular winter flu, consider that those garden-variety strains hospitalize 200,000 Americans and kill 36,000 every year. That is why Besser keeps warning that as the new variant of the H1N1 flu virus spreads to enough people, more severe illness is likely to follow.

The Associated Press contributed to this report.