World health chiefs admitted on Thursday they had yet to get a handle on swine flu and warned against any lowering of the guard after Mexico, the epicentre of the epidemic, ended a nationwide lockdown.
High schools and universities were to reopen in Mexico, the day after offices and restaurants were cleared to take down the shutters that had been ordered to remain in place for five days in a bid to contain the outbreak.
"Fortunately, we've managed to stop the dangerous expansion the virus could have had," President Felipe Calderon said during a hospital visit.
However Calderon added that "it's not time to shout victory or to say that it's now controlled and over", warning that "there will be more" cases.
Keiji Fukuda, acting director-general of the UN's World Health Organisation, acknowledged the body was still struggling to get to grips with the magnitude of the A(H1N1) virus and warned it could become more virulent later in the year with the onset of the northern hemisphere's flu season.
"It is critical for countries to maintain their alertness and monitoring so this evolution can be followed as closely as possible," Fukuda said in a videolink with Asian officials in Bangkok.
"We don't believe we have fully got a handle on the severity of the phenomenon."
The latest WHO figures show that 1,893 cases of influenza A(H1N1) infections have been reported by 23 countries.
Thirty-one people have died of the disease, all but two of them in Mexico.
Fukuda said, however, that vigilance was necessary as more countries continue to report cases on their soil. Poland and Sweden both announced their first confirmed cases of the virus on Wednesday.
Israel's health ministry reported two new cases of swine flu on Thursday, bringing to seven the total infected by the virus in the country.
"Complacency is the greatest danger," said Fukuda. "It does appear to be a period where the virus maybe seeding itself in various parts of the world.
"What we are seeing now is milder than in 1918 (when up to 50 million people died of a Spanish influenza pandemic). But the 1918 started mild in springtime and became more severe in winter."
The emergence of the virus, a new strain that has combined human, swine and bird influenza, set off fears of a worldwide pandemic, even though the death toll has been relatively low.
Countries have imposed a range of measures to prevent a global outbreak, especially hitting the tourism and travel industries and hurting Mexico's economy, already severely strained by the financial crisis.
Restrictions have also been placed on meat imports, not only in Mexico but also Canada and the United States.
Russia announced on Thursday that it was lifting a ban on imports from five US states, but also added another -- Illinois -- to the list.
The number of confirmed US cases of swine flu surged by 60 percent Wednesday to 642 from 403, with infections now reported in 41 states.
Two people have now died in the United States -- a Mexican toddler visiting relatives in Texas, and a woman in her 30s with other health problems who died in a Texas hospital on Monday.
A leading US health official warned he still expected the swine flu outbreak to reach the level of a pandemic.
"With the number of cases in other countries, I would be surprised if we don't get to level six" on the WHO's six-phase pandemic alert scale, said Richard Besser, acting head of the Centers for Disease Control and Prevention (CDC).
US health officials told lawmakers they were moving quickly to develop a vaccine and in just two weeks had gained a greater understanding of the virus.
The 2009 H1N1 virus "contains genetic pieces from four different virus sources," said Ann Schuchat, a top CDC official, adding scientists could now "identify a novel virus (and) understand its complete genetic characteristics."