The death toll rose as emergency workers dug for survivors of the 6.4-magnitude quake that toppled the 16-storey complex of almost 100 homes in the city of Tainan on Saturday.
Officials said an investigation had been launched as questions were raised over the safety of the residential blocks in the complex.
Tainan mayor William Lai said survivors and relatives had reported legal “violations" but gave no further detail.
“I’ve contacted judicial units and prosecutors have formally launched an investigation," said Lai.
“We’ve also commissioned three independent bodies to preserve evidence during the rescue so we can assist the residents if they want to file lawsuits in the future. We will hold the builder responsible if they have broken the law."
Local media reported the construction company that built the complex had gone out of business and also raised questions over the quality of the materials used.
Yueh Chin-sen, whose mother-in-law’s family of eight is still trapped, said the residents had complained of defects in the building.
“They complained that the building wasn’t well constructed as there were cracks in the walls and tiles fell off after several quakes in recent years," he told AFP.
“I hope the government will prosecute the builder on criminal charges as people lost their lives."
Rescuers said 122 residents were still missing, with 103 of them trapped “very deep" in the rubble, according to Lai.
“There’s no way to get to them direct, it’s very difficult," Lai said, adding that emergency workers were having to shore up the ruins to ensure they were secure before digging.
Several survivors were pulled from the rubble Sunday, more than 24 hours after the quake struck, as rescuers used life detectors in their desperate search.
One 20-year-old man was freed from the ruins after emergency workers spent eight hours carefully digging him out.
Census records show around 260 people living in the blocks but Lai said it was now thought that more than 300 had been inside.
Officials have said that some students renting rooms would not have been registered as living in the building, and additional family members may have returned there to celebrate the Lunar New Year holiday starting Monday.
Rescuers drilled down into the rubble Sunday, urging survivors to stay strong as they tried to reach them.
Around 200 have been rescued so far and more than 50 others were able to escape unaided.
Emergency workers used cranes, ladders and sniffer dogs to trace and extract survivors.
Among the 29 people confirmed killed by the quake, 27 died in the apartment complex collapse, including several children.
Tearful relatives huddled by the ruins, hoping for news.
Chen Yu-mei told how her three-month-old son was trapped inside with her sister’s family of seven.
“He’s a small child, I’m worried sick," she told AFP, her voice cracking and eyes red from crying.
Another woman said her son had been found dead but she was holding out hope for her daughter-in-law and two grandchildren still trapped inside.
“I won’t give up hope, I will wait here until I see them come out safe," she said.
Survivors spoke of their terror and relief.
One man told AFP how he was rescued after tapping on a wardrobe that was trapping him.
“I knocked on the closet to get the attention of rescuers who broke the window to get me," said Su Yi-ming, 48, who lived with his family on the sixth floor of the Wei-kuan complex.
Su escaped unhurt while his wife and their two children sustained minor injuries.
The quake struck at a shallow depth of 10 kilometres at around 4:00 am Saturday local time, 39 kilometres northeast of the island’s second-largest city of Kaohsiung.
Taiwan lies near the junction of two tectonic plates and is regularly hit by earthquakes.
The island’s worst tremor in recent decades was a 7.6 magnitude quake in September 1999 that killed around 2,400 people.