The magnitude 6.4 quake, which hit near the coastal city just before midnight on Tuesday, injured 260 people and caused four buildings to collapse, officials said.
Fu said the any rescue team is welcomed by people in the quake-hit areas.
"There was no problem with the materials used in the construction of the building as the structure from the fourth floor up was still intact despite the collapse", said Liu Yen-hu, president of the Hualien County Architecture Association. "I saw the first floor sink into the ground", said 35-year-old Lu Chih-son.
Tibetan spiritual leader, the Dalai Lama, has expressed sadness over the quake in Taiwan and wrote to its President Tsai Ing-wen, expressing grief over the loss of life.
Hualien is one of Taiwan's most popular tourist destinations as it lies on the picturesque east coast rail line and near the popular Taroko Gorge.
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Taiwanese rescuers braved aftershocks coursing through a dangerously leaning apartment block that was partially toppled by a deadly natural disaster, as the death toll rose to 10.
A Red Cross worker who was at the scene estimated that the building had tilted another 5 per cent overnight, and said that he had little hope of survivors being found on its lowest floors.
Meanwhile, 600 military personnel and more than 750 firefighters combed through rubble and helped with rescue efforts, according to Taiwan's Central Emergency Operation Center.
Numerous missing were believed to be still trapped inside buildings, some of which tilted precariously, after the quake struck about 22 km (14 miles) northeast of Hualien on Taiwan's east coast.
Firefighters could be seen climbing ladders hoisted against windows as they sought to reach residents inside apartments.
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Chen Chih-wei, 80, said he was sleeping in his apartment on the top floor of the building when the quake struck.
The quake hit the island nation 11:50 pm (local time) (3.50pm GMT) on Tuesday, around 21 kilometres, northeast of the port city of Hualien, according to the United States Geological Survey (USGS).
The natural disaster followed one over the weekend off the coast of Hualien, which lies along the famed "Pacific Rim of Fire" known for seismic activity from Alaska to Southeast Asia.
The island is regularly rocked by earthquakes.
At least six people were killed, 256 were injured and 76 could not be contacted after the shallow, magnitude 6.4 quake late Tuesday night.
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A 30-year-old woman said it is possible to know when storms will end but that is not true of quakes. "I was sleeping and suddenly I was standing", he told AFP.