The WHO had raised its alert to five on a scale of six, signalling that a pandemic was "imminent" after Mexico and the US showed sustained local transmission of the H1N1 virus.
Keiji Fukuda, acting assistant director-general of the global health body, said: "If countries had not been thinking about what to do in this kind of situation, the fact is we would have had much more confusion."
"In many ways, the severity would have been greater."
The WHO confirmed that the global death toll from the flu now stands at 61 after Costa Rica reported its first fatality and the US confirmed a third death.
Thailand's first two cases involved patients who had travelled to Mexico.
Finland also confirmed its first two cases on Tuesday while Cuba had earlier reported its first case in a Mexican student.
Cuba's health minsitry said the student was one of a group of 14 Mexicans studying in Havana, the capital, who were tested for the disease.
Canada also confirmed 40 new cases, bringing the total number recorded by national authorities there to 331.
Attention is now focused on China, where authorities confirmed that a 30-year-old man was hospitalised with the virus after arriving in the southwestern city of Chengdu on a flight from the US.
|China has ordered the stepping up of flu monitoring across the country [AFP]
"This is our country's first case of H1N1," Mao Qunan, a Chinese health ministry spokesman, said on Monday.
Beijing ordered the stepping up of flu monitoring nationwide on Tuesday and said it had found and isolated nearly all those who travelled on flights with the man.
Last week, officials in Hong Kong ended the quarantine of nearly 300 hotel guests and staff after a week under medical observation following a Mexican guest being confirmed with H1N1.
Health officials in the United States reported that the 2,600 confirmed cases across the country represented just the tip of the iceberg of actual infections.
Anne Schuchat, the interim deputy director at the Centres for Disease Control and Prevention, said: "Many states did not report over the weekend, so we expect a big jump in the number of cases tomorrow."
Most of the 5,251 laboratory-confirmed cases recorded by the WHO in some 30 countries have involved relatively mild symptoms and the virus has proved to be treatable with anti-viral drugs such as Tamiflu so far.
Roche, the Swiss drugs giant, has said that it was donating 5.65 million treatment courses of Tamiflu to help fight the outbreak.