Photos and videos posted on social media show toppled and leaning high-rise buildings and badly damaged roads.
More than 100 were killed in a quake in southern Taiwan in 2016, and some Taiwanese remain scarred by a 1999 natural disaster with 7.6 magnitude whose impact was felt across the island and in which more than 2,000 people died.
The quake was centered in the East China Sea about 21 kilometers north-northeast of Hualien City.
Premier William Lai said two people had died in the quake in the port city of Hualien and 114 were injured, some seriously.
But the quake took down a multi-story building and an official from the Ministry of Interior's fire station division told Reuters that people were trapped.
Taiwan's Central News Agency reported that the ground floor of the Marshal Hotel, a building in Hualien district, had caved in and three people were believed to be trapped inside. We dare not go back home now.
The quake caused widespread damage in Hualien, a city of 100,000 people. "There are many aftershocks and we are anxious the house is damaged".
Clarke said everyone in the hostel is out and there have been a couple of aftershocks.
It follows nearly 100 smaller tremors to have hit the area in the last three days and comes exactly two years since a quake of the same magnitude struck the southern Taiwanese city of Tainan, killing more than 100 people. The quake, which was one of the deadliest in the world had struck about 30 km south of the Iraqi town Darbandikhan, near the north-eastern border with Iran.
Other buildings shifted on their foundations and rescuers used ladders, ropes and cranes to get residents to safety.
Taiwan lies near the junction of two tectonic plates and is regularly hit by earthquakes.
A magnitude-7.6 quake in central Taiwan killed more than 2,300 people in 1999.
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