Rescue workers remove the first of two bodies of a Hong Kong Canadian couple from the Yun Tsui building, which is leaning at a precarious angle, in the Taiwanese city of Hualien on February 9, 2018, after the city was hit by a 6.4-magnitude quake late on February 6.
Hualien officials say there are no people trapped in other buildings.
"The rescuers have detected further shifts in the building [where survivors are trapped], and fear there might be a further collapse", he said.
Among the injured were mainland Chinese, Czech, Japanese, Singaporean and South Korean nationals. One aftershock shortly before midnight measured 5.7-magnitude.
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 in a single apartment block which collapsed.
"Even if the golden 72 hours are slipping away and there is only a 0.1 percent chance (of saving them), we will continue to search for the five Chinese tourists who remain missing", he said.
Water supply had returned to almost 5,000 homes by noon (local time), while power was restored to about 1,700 households.
"We were still open when it happened", said Lin Ching-wen, who operates a restaurant near a damaged military hospital.
A Reuters video showed large cracks in the road, while police and emergency services tried to help anxious people roaming the streets.
At the Yunmen Tsuiti building, clothes and other personal items were visible on the balconies as the rescue work continued.
"The President has asked the cabinet and related ministries to immediately launch the "disaster mechanism" and to work at the fastest rate on disaster relief work", Mr Tsai's office said in a statement.
The Government of Saint Lucia has expressed condolences to the Government and People of the Republic of China (ROC) Taiwan, following a 6.4 magnitude quake which has left several dead and some still missing. The island's Central Weather Bureau put the magnitude at 6.0.