Mexico's leadership in the global battle against swine flu has saved "thousands of lives," President Felipe Calderon has said, as experts warned the disease could re-emerge in a more virulent form.
Even as Mexico's government said it had brought the spread of the A(H1N1) virus under control, the United States and the United Nations urged continued vigilance as the number of human infections worldwide passed the 1,000 mark.
The World Health Organization (WHO) now says the epidemic has affected people in 21 countries.
Calderon, in a televised address late Monday, said Mexico had "taken the lead in the global battles against the virus".
Thanks to its "responsible" actions, "thousands of lives have been saved not only in Mexico but in the world," he said, adding that businesses, schools and museums closed for more than a week would begin to reopen from Wednesday.
The Mexican leader urged citizens to remain vigilant, saying: "This virus is still circulating."
That note of caution was repeated in Washington, where White House spokesman Robert Gibbs told reporters: "It's still out there."
"Certainly you're always hopeful that what you plan for may never come to fruition. But the key is to prepare for any outcome and be prepared to address it," he said.
The WHO has reported a total of 1,085 cases worldwide and 26 deaths, 25 of them in Mexico and one in the United States. Mexico puts its death toll at 26.
Acting WHO director-general Keiji Fukuda said: "In this situation, it's critical that we continue to maintain and strengthen our alert and surveillance."
WHO chief Margaret Chan told UN officials in New York that despite the continued spread of the flu virus, a pandemic could not yet be declared.
"We don't know how long we have till we move to phase six. Six indicates we are in a pandemic. We are not there yet," she said.
Chan said the end of the flu season in the northern hemisphere meant that while any initial outbreak could be milder, a second wave could be more lethal, reflecting a pattern seen with the 1918 Spanish flu pandemic that killed up to 50 million people.
Its re-emergence "would be the biggest of all outbreaks the world has faced in the 21st century," she told the Financial Times.
UN chief Ban Ki-moon echoed appeals for caution, saying at the UN talks: "There is still much that is not known about this new strain and the dangers it poses... In the face of uncertainty, we must be vigilant."
Portugal became the latest European country to record a case of swine flu, while France announced two new confirmed cases as did Italy, doubling their previous caseloads. Britain put its case total at 27.
In China, the centre of the 2003 SARS outbreak, the government has come under diplomatic pressure after it quarantined foreigners in what it said was a bid to contain the disease.
Mexican travellers held at a Beijing hotel said they were told by their embassy to be ready to leave Tuesday, ending an enforced isolation that Mexico charged was unfairly targeting its citizens.
"We were told to be ready to go. We are just awaiting word," Gustavo Carrillo, a Mexican businessman, told AFP.
Mexican diplomats have complained to China that 70 of their countrymen were placed under seven-day isolation across China despite showing no signs of (A)H1N1.
A chartered AeroMexico airliner arrived in Shanghai on Tuesday to repatriate dozens of Mexican nationals.
Canada has asked Beijing to explain the quarantine of a group of Canadian students, Foreign Minister Lawrence Cannon said on Monday.
Despite showing no symptoms of infection from the virus and having no fever, they were told they would be quarantined for seven days at a local hotel, the CBC said, citing an email from one of the students.
In Hong Kong, the scene of Asia's first confirmed swine flu case, chief executive Donald Tsang on Tuesday apologised to guests quarantined in a city hotel for seven days, while defending the decision to isolate them.
Hong Kong's Metropark hotel, and the 300 staff and guests inside, has been sealed off since last Friday following the discovery that a Mexican visitor had tested positive for the A(H1N1) virus.
"What we have done is in the interests of both themselves and the public health," Tsang told reporters.
"Our thanks and apologies go in particular to those in the Metropark hotel. You are our guests. We can appreciate the boredom, frustration and dissatisfaction that the quarantine may have caused you."