At the crash site, efforts are now under way to identify everyone onboard. The cause of the crash has not yet been identified, Fay reported.
The aircraft was an MD-82, operated by budget airline One-Two-Go, and was carrying foreign holidaymakers, many of them Europeans, to the island.
The aircraft attempted to land during heavy rain, but broke into two and burst into flames on the runway.
Thai television broadcast images of its crumpled fuselage.
Hospital officials said eight Britons, eight Thais, five Germans and two Australians were among the survivors.
|The MD-82 aircraft was flying to |
Phuket from the capital, Bangkok
Chiasak Angkauwan, a civil aviation official, told Thai television: "The first part of the plane is dug into the ground. The tail section is stuck on the runway.
"The airplane asked to land, but due to the weather in Phuket - strong wind and heavy rain - maybe the pilot did not see the runway clearly."
Lieutenant-Major Sokchai Limcharoen, a police chief in the Phuket area, said the aircraft crashed at 3:35pm (0835 GMT).
"The plane was landing and slid off the runway. We are rescuing people and carrying injured people to hospitals," he said.
Nong Khaonual, a Thai who survived the crash with his wife, said he believed the aircraft had descended too quickly.
"The airplane was landing in heavy rain. It landed too fast. I have never seen anything like this. It descended very fast," he told Nation Television in hospital.
"Just before we touched the runway we felt the plane try to lift up, and it skidded off the runway.
"My wife was half conscious and I dragged her out of the emergency exit. There was a man behind us and he was on fire."
Another survivor, an Irishman named John, described the attempts to land in atrocious conditions.
"You could tell there was a problem. The plane was flying around trying to land. It was making some noises and it was bad rain," John, who was travelling with a friend who also survived, told Thailand's ITV television channel.
"The plane was on fire, but I managed to get through."