Mexico, with 1,626 confirmed cases, is trying to get back to normal
The US now has 2,532 confirmed cases of swine flu, after a jump in figures in recent days, officials say.
The cases - up around 600 since Friday - mean the US has now surpassed Mexico as the most affected nation.
But the total of three confirmed deaths is far lower than in Mexico where 48 people are known to have died.
In Mexico, people worked over the weekend to clean and disinfect primary schools which are due to resume classes after a two-week break.
However, several Mexican states are delaying the return to school for another week amid more suspected new cases.
Secondary schools and universities re-opened last week as part of a gradual resumption of business after a shutdown of several days ordered by the Mexican government in a bid to stem the outbreak.
Mexico, where the swine flu outbreak first came to light, has 1,626 confirmed cases. Globally, the figure stands at more than 4,300 across 30 countries. This includes China which on Monday reported its first case on the Chinese mainland.
Most of the cases in the US have been mild. The third death in the US was reported on Saturday - a man in his 30s with a heart condition, officials said.
Officials warn that the virus has still to run its course.
"More cases, more hospitalisations and more deaths from this outbreak will occur over the coming days and weeks, " a CDC statement said.
A jump in confirmed cases is also likely because the CDC has developed a kit for testing that is being distributed across the US and Puerto Rico, as well as internationally.
"This increase in testing capacity is likely to result in an increase in the number of reported confirmed cases in this country, which should provide a more accurate picture of the burden of disease in the United States," the CDC said.