Numerous missing were believed to be still trapped inside buildings, some of which were tilting precariously, after the quake hit about 22 km (14 miles) northeast of Hualien on Taiwan's east coast.
"We will do our best to find the missing people within the 72-hour golden rescue period, " Fu said.
The 12 victims include four from Chinese mainland, five from Taiwan, one from the Philippines and two from Canada.
The National Fire Agency revised the death toll down to nine people after rescuers double-counted one person who died.
The shifting of the buildings after the magnitude 6.4 quake late Tuesday night was likely caused by soil liquefaction, when the ground beneath a building loses its solidity under stress such as that caused by an natural disaster.
"Our thoughts are with the people of Hualien, and their friends and family, including those of the two Canadians who lost their lives", the Canadian Trade Office in Taipei said in a statement.
The buildings, which include an 11-storey hotel, have been cleared of people and are being demolished "in order to maintain safety for the public", Hualien mayor Fu Kun-chi said, adding that the authorities are probing possible construction irregularities. Ongoing tremors are also hampering the rescue effort. The quake also buckled roads and disrupted electricity and water supplies to thousands of households.More news: Despite Trump's attacks, Obamacare sign-ups for 2018 hold steady
A maintenance worker who was rescued after being trapped in the basement of the Marshal Hotel said the force of the quake was unusual even for a region used to temblors.
"We hope local people will overcome the difficulties and rebuild their homes at an early date", he said.
The highway from Suao to Hualien was temporarily closed.
Chen Deming, president of the mainland-based Association for Relations Across the Taiwan Straits, said the mainland is willing to assist with the quake relief, including sending rescue teams to the island.
Hualien policeman Cheng Po-jen was on duty Tuesday night when a magnitude 6.0 quake struck the eastern Taiwan city, causing four buildings to partially collapse including the one in which Cheng lived. Five people involved in constructing the complex were found guilty of negligence and given prison sentences.
A magnitude 7.7 temblor hit the central county of Nantou in September 1999, killing more than 2,400 people.