At least four people including an eight-year-old girl have been rescued from a high-rise Taiwanese apartment building toppled by a powerful earthquake two days earlier.

More than 100 people are believed to still be under the debris in a disaster that struck during the most important family holiday in the Chinese calendar - the Lunar New Year.

Saturday's quake killed at least 38 people in Tainan city in southern Taiwan, all but two of them in the collapse of the 17-storey building. Even though the 6.4-magnitude quake was shallow, few buildings were damaged, which experts said was because Taiwan's building standards are high.

Authorities have rescued more than 170 people - the vast majority in the immediate hours after the quake - using information about the building layout and the possible location of those trapped.

Five survivors are believed to have been pulled out on Sunday, and at least four on Monday. One of them, Tsao Wei-ling, called out "Here I am" as rescuers dug through to find her,.

She was found under the body of her husband, who had shielded her from a collapsed beam. Ms Tsao's husband and two-year-son were found dead, and five other members of the family remain unaccounted for.

Teams also rescued a 42-year-old man and an eight-year-old girl, who had been trapped for more than 61 hours.

Mayor Lai Ching-Te told reporters he had briefly exchanged words with the girl, Lin Su-chin.

"She is awake, but looks dehydrated, lost some temperature but she's awake and her blood pressure is okay," he said. "I asked her if there's anything wrong with her body. She shook her head."

Shortly afterwards, rescue workers also pulled out a 28-year-old Vietnamese woman, identified as Chen Mei-jih, who had been trapped on what was the building's fifth floor.

Family members of the missing flooded into the information centre to wait for news of their loved ones.

Tensions rose as some relatives, losing patience, demanded to speak to rescue workers directly to get the latest information.

Earthquakes rattle Taiwan frequently. Most are minor and cause little or no damage, though a magnitude-7.6 quake in central Taiwan in 1999 killed more than 2,300 people.

The spectacular fall of the high-rise, built in 1989, raised questions about its construction. The government says it will investigate whether the developer cut corners.

Huang Jia-rui, a structural engineer in Tainan, said Taiwan's buildings are not as safe as Japan's, which is a leader in engineering quake-proof structures, but the island is catching up.

The extended Lunar New Year holiday officially started on Monday, but celebrations were subdued and President Ma Ying-jeou and president-elect Tsai Ing-wen cancelled the traditional handing out of envelopes of cash in their home towns.