It had been just about 24 hours since a magnitude 6.4 quake rattled Taiwan's east coast, crumbling walls and knocking tall buildings askew, when rescue workers felt another big rumble late Wednesday.
The U.S. Geological Survey said the quake struck just before midnight Tuesday about 21 kilometre northeast of Hualien at a relatively shallow depth of about 10.6 kilometres.
Cellphone video from Hualien City shows a large building leaning at a unsafe angle as sirens are heard in the background.
On Wednesday a clearer toll emerged: six dead and dozens of people feared trapped, officials said.
With aftershocks continuing through the night, residents were being directed to shelters, including a newly built baseball stadium, where beds and hot food were provided.
"We will not rest until all are found", she added.
A Reuters witness said people rushed out of a residential building and rescue workers looked up from piles of debris after another strong aftershock rattled the city at around 11 a.m. on Thursday (0300 GMT).
Among the several badly damaged buildings was a hospital, local media reports.
The government would subsidize people who need to relocate in accordance with due procedure, he said.
Search teams managed to rescue 235 people, trapped under the rubble of collapsed buildings in Hualien, including the worst-hit Yunmen Cuidi building and Hotel Tongshuai, where the lower floors had collapsed completely. Two Singaporeans were affected by the quake, Taiwanese officials said.
No deaths or injuries have been reported in mainland China.
Nearly 100 weaker earthquakes were dectected along Taiwan's east coast in the last week.
The mountainous east coast of Taiwan is less populated than its flatter western side. The region is known for its natural beauty.
The highway from Suao to Hualien was temporarily closed.
At least one bridge, badly damaged by the quake, has been partially reopened by police to traffic, Taiwan's official news agency CNA said.
Lai made the announcement while presiding over an ad hoc meeting at the Central Emergency Operation Center in New Taipei City, which is coordinating rescue efforts and assessing damage in the aftermath of the magnitude 6.0 quake.