Largely rural and sparsely populated Hualien was hit by a 7.2 magnitude earthquake on April 3 that killed at least 17 people, and there have been more than 1000 aftershocks since.
Buildings across large parts of northern, eastern and western Taiwan, including in the capital Taipei, swayed throughout the night on Monday and Tuesday, with the largest quake measuring a 6.3 magnitude.
All were very shallow.
Taiwanese weather officials say the latest quakes are aftershocks from the large April 3 quake. (EPA PHOTO)
"Especially at 2am, it shook very strongly," Taipei resident Aden Peng, 44, said.
"In fact, for a moment even I thought about rushing downstairs, but as we live on the sixth floor, I felt it a bit troublesome to go down.
"Then again, according to my previous experience, I thought it should be fine and hoped it would be fine," the medical researcher said.
"And because I was very tired, I just continued to sleep, hoping for the best."
Taiwan's Central Weather Administration said the spate of earthquakes starting on Monday afternoon - which it put at more than 200 - were aftershocks from the large April 3 quake.
Seismological Centre Director Wu Chien-fu told reporters that the aftershocks were a "concentrated release of energy" and that more could be expected, although perhaps not as strong.
With heavy rain predicted for all of Taiwan this week, people in Hualien need to be prepared for further disruption, he said.
Taiwan lies near the junction of two tectonic plates and is prone to earthquakes. (AP PHOTO)
Taiwan President Tsai Ing-wen, writing on her Facebook page, called on people to avoid the mountains and to stay alert.
"When an earthquake occurs, don't panic," she wrote.
"Master the principle of 'duck, cover, stay put'."
The Hualien fire department said two buildings, already uninhabited after being damaged on April 3, suffered further damage and were leaning.
There were no reports of casualties.
The world's largest contract chipmaker, Taiwan Semiconductor Manufacturing Co (TSMC) , whose factories are on the island's western coast, said some staff at a small number of factories were evacuated, but facility and safety systems were functioning normally and all personnel were safe.
"Currently, we do not expect any impact on operations," it said in an email.
Investors brushed off concerns about the quake, with TSMC's Taipei-listed shares closing up 1.6 per cent on Tuesday.
In mountainous Hualien county, rockfalls closed roads and the government suspended work and school for the day.
Taiwan lies near the junction of two tectonic plates and is prone to earthquakes.
More than 100 people were killed in a quake in southern Taiwan in 2016, while a 7.3 magnitude quake killed more than 2000 people in 1999.
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