Dr Besser said more information was needed to determine the extent of the threat posed by the virus but that "concern has grown" since Thursday as more information has come to light.
He said it was not yet known whether swine flu would lead to a major pandemic but that scientists around the world were monitoring developments and taking the threat seriously.
"At the early stages of an outbreak there is much uncertainty and probably more than everyone would like. Our guidelines and advice are likely to be interim and fluid and subject to change as we learn more," he said.
Both the CDC and the WHO say they plan to send experts to Mexico to help investigate the virus.
Swine flu is a respiratory disease which infects pigs. It does not normally infect humans, although sporadic cases do occur usually in people who have had close contact with pigs.
There have also been rare documented cases of humans passing the infection to other humans.
Such cases are monitored very closely because of fears that a new strain of swine flu with the ability to pass from person to person could spark a pandemic.
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