The number of flu cases in Mexico City appears to be stabilizing and could lead officials to downgrade the maximum alert on the capital, the City's Mayor, Marcelo Ebrard, said on Wednesday.

"The number of infectious cases seems to be stabilizing," he told reporters.

If that is confirmed, "we could lower our maximum alert level to just an alert," he said.

The capital has been the most-affected part of Mexico in the swine flu outbreak, prompting authorities to close all bars, clubs, restaurants, gyms, cinemas and other venues where people gather.

According to a national toll given late Tuesday by Health Minister Jose Angel Cordova after World Health Organization testing, there have been seven confirmed deaths from the A/H1N1 swine flu virus.

But nearly 160 deaths in total have been blamed on the disease and testing of those cases is continuing.

Hospitals are treating more than 1300 people showing symptoms of the virus.