TAINAN: Rescuers pulled out alive an eight-year-old girl and her aunt from the rubble of a Taiwan apartment block on Monday, more than 60 hours after it was toppled by a quake, as the mayor of the southern city of Tainan warned the death toll could exceed 100.

The official death toll from the quake rose to 38, with more than 100 people missing.

The girl, named as Lin Su-Chin, was conscious and had been taken to hospital, Taiwan television stations said. Her aunt, Chen Mei-jih, was rescued shortly after.

The quake struck at about 4 a.m. on Saturday (2000 GMT Friday) at the beginning of the Lunar New Year holiday, with almost all the dead found in Tainan's toppled Wei-guan Golden Dragon Building.

Rescue efforts are focused on the wreckage of the 17-storey building, where more than 100 people are listed as missing and are suspected to be buried deep under the rubble.

Earlier, Wang Ting-yu, a legislator who represents the area, told reporters that a woman, identified as Tsao Wei-ling, was found alive, lying under her dead husband. Their two-year-old son, who was also killed, was found nearby.

Another survivor, a man named Li Tsung-tian, was pulled out later, with Taiwan television stations showing live images of the rescues. Several hours later, Li's girlfriend was found dead in the rubble.

Tsao and Li were both being treated in hospital.

Tainan Mayor William Lai said during a visit to a funeral home that rescue efforts had entered what he called the "third stage".

"There are more fatalities than those pulled out (alive), and the number of fatalities will probably exceed 100," Lai told reporters.

Rescuers continued to scramble over the twisted wreckage of the building as numbed family members stood around, waiting for news of missing relatives.

Taiwan's government said in a statement 36 of the 38 dead were from the Wei-guan building, which was built in 1994.

President-elect Tsai Ing-wen, who won election last month, said there needed to be a "general sorting out" of old buildings to make sure they were able to cope with disasters like earthquakes.

"There needs to be a continued strengthening of their ability to deal with disasters," she said.

Outgoing President Ma Ying-jeou, speaking to reporters at a Tainan hospital, said the government needed to be a better job in ensuring building quality.

"In the near future, regarding building management, we will have some further improvements. We will definitely do this work well," Ma said.

Reuters witnesses at the scene of the collapse saw large rectangular, commercial cans of cooking-oil packed inside wall cavities exposed by the damage, apparently having been used as building material.

Chinese President Xi Jinping also conveyed condolences to the victims, state news agency Xinhua reported late on Sunday, and repeated Beijing's offer to provide help.

China views self-ruled Taiwan as a wayward province, to be bought under its control by force if necessary.