Asked about assertions by Mexican officials that the A/H1N1 outbreak may have peaked in Mexico, Napolitano said, "I have no reason to think that is inaccurate."
Latest report from the U.S. Centers for Disease Control and Prevention said there are now 286 confirmed cases in 36 states -- 60 more from last Sunday.
Worldwide, the number of confirmed cases of the A/H1N1 flu has topped 1,085.
The virus has been responsible for 25 deaths in Mexico and one in the United States so far.
The U.S. authorities said the possibility remains that the A/H1N1 virus could stage a comeback in the fall in a stronger form.
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Editor:Yang Jie