U.S. authorities report that the number of confirmed swine flu cases in the United States has reached 286 across 36 states.  But the Obama administration says it is cautiously optimistic that the outbreak of swine influenza A H1N1 virus will be mild - at least for now.  

The countries hardest-hit by swine flu - Mexico and the United States - are reporting some encouraging signs after weeks of fear that grew more intense each day.  Mexican officials say the number of people contracting the virus has leveled off, and that schools and other public places will reopen next week.

Although the virus continues to spread across the United States, the extent of the outbreak remains limited and most flu sufferers report relatively mild symptoms.

Homeland Security Secretary Janet Napolitano gave a "cautiously optimistic" outlook.

"We have started to see encouraging signs that this virus may be mild, and its spread may be limited," said Janet Napolitano.

At the same time, no one is declaring victory over swine flu.  The Acting Director of the U.S. Centers for Disease Control and Prevention, Richard Besser, said it was too early to say that the situation is under control.

Secretary Napolitano added that vigilance and concerted efforts to contain the disease must continue.  She said that even if the current outbreak fades, the world may not have seen the last of the new influenza strain.

"H1N1 flu could die down soon and return later again this fall when the [northern hemisphere] flu season enters back in full swing," she said.

U.S. health officials say research is going forward that will allow development of a swine flu vaccine.  But they add that no decision has been made on mass-inoculations in the United States.

At a White House social gathering on the eve of Mexico's independence day, President Barack Obama paid tribute to U.S.-Mexico cooperation in battling swine flu.

"Good neighbors work together when faced with common challenges," he said. "And that is why we are working closely with the Mexican government to identify and treat illnesses that are caused by this new flu strain.  I spoke with [Mexican] President [Felipe] Calderon Saturday about this new approach."

Mexico's ambassador to the United States, Arturo Sarukhan, echoed that sentiment, saying the swine flu outbreak has again demonstrated how a productive U.S.-Mexican relationship is vital to both nations.

Swine flu cases have been reported in more than 20 nations, including Colombia - the first South American nation to see an H1N1 infection.  Health officials note that, while the regular flu season has come to an end in the northern hemisphere, it is just beginning south of the equator.