Thailand and Finland are the latest countries to report confirmed cases of swine flu.
All the patients involved had recently travelled to Mexico.
The Finnish authorities said all close relatives of the two Helsinki cases were uninfected, and other contacts were being traced.
In Bangkok, a number of contacts of each of the two cases there are being kept under surveillance.
The World Health Organization says the latest worldwide total of confirmed cases of the influenza A (H1N1) virus is 5,251, in 30 countries, of whom 61 have died.
Swiss drugs giant Roche says it is donating 5.65m treatment courses of its anti-viral drug Tamiflu to help the WHO fight the outbreak.
The company added that it would also boost its production capacity for anti-virals, producing another 110m treatment courses over the next five months.
Following that, it will further ramp up capacity to a maximum of 36m treatments per month by the end of the year if required.
However, the WHO said swine flu could still mutate into a more virulent form and spark an influenza pandemic that could be expected to circle the globe up to three times.
The impact of any pandemic would vary, as a virus that causes only mild illness in countries with strong health systems can become devastating in those with weak health systems, shortages of drugs and poorly equipped hospitals.
So far, with the exception of the outbreak in Mexico, the virus has tended to cause very mild illness in otherwise healthy people, the WHO said.
But influenza viruses mutate frequently and unpredictably and the emergence of an inherently more virulent virus during the course of a pandemic cannot be ruled out.