At least nine people were killed when the powerful quake hit the popular eastern tourist city of Hualien late Tuesday.
Dozens were still missing on Thursday.
The major focus for emergency workers remained the 12-storey Yun Tsui apartment block where six of the deaths occurred and dozens are still missing.
The lower floors of the tower, which also housed a hotel, pancaked, leaving the structure leaning at a 50-degree angle and sparking fears of imminent collapse.
At least 58 people remain unaccounted for across the city, the national fire agency said.
More than 250 people were injured in the tremor, the strongest to hit Hualien in decades.
A handful of other buildings were badly damaged, roads were torn up and hundreds of people were forced to shelter in schools and a stadium.
The government said 17 foreigners sought medical treatment for minor injuries.
The Hualien quake came exactly two years to the day after a similar sized tremor struck the western city of Tainan, killing 117 people.
Most of those who perished died in a single apartment block which collapsed.
Five people were later found guilty over the disaster, including the developer and two architects, for building an inadequate structure.