Two people were pulled alive from the rubble of an apartment complex in Taiwan Monday, more than 50 hours after it was felled by a powerful earthquake, as rescuers scrabbled to find 100 more still missing.

The rescues came as fears grow for more than 100 buried deep in the rubble of the Wei-kuan building in the southern city of Tainan, which was toppled Saturday.

The 6.4-magnitude quake left 37 confirmed dead, most of them from the apartment complex.

One man was lifted out by crane Monday and a woman was also freed after rescuers heard her cries for help.

The male survivor was named by officials as 40-year-old Lee Tsong-tian -- rescuers told how they had been trying to dig him out of the rubble for more than 20 hours but were unable to do so as he was trapped by his leg.

Doctors had been sent in to assess whether removing his leg would help save him, but felt there was not enough room for the operation.

He was eventually freed, but may need his leg amputated.

Tainan mayor William Lai said he talked to Lee just after he was rescued.

"I briefly chatted with him and he could communicate with his sister," he said.

"But I'm afraid his left leg might need emergency treatment... it is not immediately clear whether he'll be able to keep his leg, but doctors will do everything to treat him."

The woman survivor was named as Tsao Wei-ling, 45, and is in a stable condition -- her husband and two-year-old child were pulled out dead from the rubble, officials at the site said, with a search ongoing for five other members of her family trapped inside.

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'Hearts sinking'

Taiwan's President Ma Ying-jeou said there was still hope for survivors, even beyond the first 72-hour rescue window, the most likely time for people to be found alive.

"We will carry on until the last second. The golden 72 hours of rescue is the standard, but there are many exceptions," said Ma after visiting two survivors at a Tainan hospital who are in a stable condition, with fractured bones.

One of them had lost her 10-day old baby and husband. Her two other children remain missing

The other had lost her husband, while her son and pregnant daughter-in-law are missing.

READ: Taiwan quake: Death toll increases to 35, over 100 remain missing

"Many people are still trapped and our hearts are sinking," said Ma.

Tainan deputy mayor Yen Chun-tso who visited the hospital with Ma added: "More than 100 people are trapped at the bottom and every single one of them is a challenge", but pledged rescuers would not give up.

Cranes, drills, ladders, sniffer dogs and life detector equipment are being used to trace and extract the trapped, though with the building precarious, emergency workers and soldiers have also had to spend time bolstering the ruins.

Rescuers are set to start using diggers and extractors to remove giant concrete slabs once they have ensured all residents from the upper parts of the rubble have been freed.

Traditionally a time of celebration and reunion, officials say many relatives would have joined their families in the Wei-kuan complex to enjoy the holidays, upping the number inside.

Now, instead of celebrations, many relatives endure a grim wait at the site for news of the missing.

Hung Yueh-yu said his brother was rescued on the first day, but his sister-in law and nephew are trapped.

"I'm worried and I will keep waiting for their news -- I think rescuers are working really hard. I'm hoping for the best," he said.

Prosecutors have launched an investigation into the building collapse after questions were raised by survivors, relatives and media over its safety.

President-elect Tsai Ing-wen, who will take the reins in May, said the new government would prioritise building safety.

"There are many old buildings across Taiwan... there should be an overall review of their resistance to earthquakes and other disasters," she said during a hospital visit to survivors.