Mexican health authorities said Saturday there have been three new deaths from H1N1 flu, and the number of confirmed cases has grown to 473.
The official death toll now stands at 19.
Mexican Health Secretary Jose Angel Cordova urged citizens not to let their guard down against the virus which has spread into Europe and Asia.
Some experts say the virus could mutate into something more deadly, as most cases outside of Mexico have been mild.
Meanwhile, across the planet in a Hong Kong hotel, hundreds of guests and employees are under quarantine after a tourist from Mexico tested positive for H1N1, while Costa Rica, South Korea and Italy confirmed their first cases of the virus.
The guest fell ill on Thursday after arriving in Hong Kong from Mexico via Shanghai.
Hong Kong health authorities in protective body suits could be seen in the lobby of the Metropark Hotel on Saturday morning, as guests picked up breakfast provisions before going back to their rooms.
A tourist who had left the hotel to spend the night with friends returned to the hotel on Saturday and will also remain in quarantine.
The hotel was cordoned off with police tape, while officers wearing face masks guarded the entranceways.
Health workers examined the 200 guests and staff, 60 of whom exhibited mild symptoms and were taken to hospital for further check-ups, according to Thomas Tsang, controller of Hong Kong's Center of Health Protection.
While some guests felt the quarantine was an overreaction, Hong Kong leader Donald Tsang defended the government's decision.
"Given the current situation, I'd rather err on the side of caution than miss the opportunity to contain the disease," Tsang said late Friday.
Officials in China, Taiwan and Hong Kong raced to identify who the infected traveller may have had contact with during his flight from Mexico to Shanghai and then from Shanghai to Hong Kong.
The unidentified man arrived in Shanghai aboard AeroMexico flight AM 98 and few to Hong Kong on China Eastern Airlines flight MU 505.
He developed a fever after he arrived in Hong Kong and is now in isolation in hospital in stable condition.
Officials were attempting to locate another 11 people who arrived in Shanghai from Mexico on Thursday before travelling to southern China.
Costa Rica confirmed its first case of the virus Saturday, but the patient is apparently not in danger. It's also the first confirmation of H1N1 in Latin America outside Mexico.
South Korea also confirmed its first case of H1N1 flu Saturday, according to Lee Jong-koo, head of the state disease control centre.
The patient, who officials identified only as a 51-year-old woman, returned from Mexico on April 26. The next day, she said she was experiencing flu-like symptoms. She was in good condition under quarantine, a doctor who is treating her told reporters.
In Italy, a patient at the Massa Carara Hospital in Tuscany has tested positive for the H1N1 virus.
Giuliano Biselli, the hospital's health director, told the Associated Press that the national health institute laboratory in Rome confirmed diagnosis.
According to Biselli, the man is recovering but will remain in hospital for a few days.
Italy's Health Ministry has declined to comment on the case until a news conference scheduled for later Saturday, but the Apcom news agency said Tuscan officials confirmed the man had travelled to Mexico.
There are more than 600 confirmed cases of H1N1 flu worldwide, although the true number is suspected to be much higher.
In response to the outbreak, the WHO raised its alert level to Phase 5 Wednesday, meaning the probability of a pandemic is "high to certain."
