At least four midsized buildings in worst-hit Hualien county leaned at sharp angles, their lowest floors crushed into mangled heaps of concrete, glass, iron and other debris.
Emergency workers surrounded a badly damaged 12-storey residential building, a major focus of the rescue effort.
Noting the support received from the people of Taiwan during the March 2011 quake and tsunami disaster in northeastern Japan, Abe said in the message that Japan "wants to give whatever assistance is needed".
Nervous residents have since endured more than 200 aftershocks, including a 5.7 quake on Wednesday and smaller tremors early today.
A magnitude 5.7 quake shook the already devastated town in the early hours of Thursday, Taiwan's official news agency Central News Agency said, the largest in a series of aftershocks. They sent the rescue teams scurrying from the building, only for them to return a little later and resume their grim task.
An emergency responder surnamed Lin said it took 14 hours to free the body of the hotel worker, who was partially trapped between the hotel's ceiling and floor.
A maintenance worker who was rescued after being trapped in the basement of the Marshal Hotel, whose ground floor had caved in, said the force of the natural disaster was unusual.
One of the people killed at the apartment block was a woman from mainland China, authorities said.
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Tualien lies close to Taiwan's east coast.
"It is true that we don't need external manpower and resources because we have all these things", he said, adding that the government accepted help from Japan because it had cutting-edge equipment that would make the search for survivors more effective.
Of the victims, four came from the Chinese mainland and one from the Philippines. The victims were a 66-year-old male and a 60-year-old female. She passed away Wednesday evening after suffering a head injury during the quake, the news agency reported.
The agency says 219 people were injured, two dozen of them critically, in Hualien county.
The authorities "would not give up" on disaster relief efforts, Taiwan's President Tsai Ing-wen said yesterday during her second visit to the quake-hit area.
"I didn't really dare stay at home", said Hualien resident Yang Yantin.
It said the team is headed to Hualien, Taiwan to facilitate the handling of the remains.
The biggest quake in recent memory was a 7.3 temblor that killed 2,400 people in 1999.