Taiwan's quake-hit eastern county of Hualien was rattled by dozens of aftershocks late on Monday and early on Tuesday, but only minor damage was reported and no casualties and major chipmaker TSMC said it saw no impact on operations.

Largely rural and sparsely populated Hualien was hit by a 7.2 magnitude earthquake on April 3 that killed at least 14 people, and there have been more than 1,000 aftershocks since.

Buildings across large parts of northern, eastern and western Taiwan, including in the capital, Taipei, swayed throughout the night, with the largest quake measuring a 6.3 magnitude. All were very shallow.

Taiwan's Central Weather Administration said the spate of earthquakes starting Monday afternoon - which it put at about 180 - were aftershocks from the large April 3 quake.

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 contact 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 up 1.75% on Tuesday morning.

In mountainous Hualien county, some road closings following rockfalls were reported, 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 2,000 people in 1999.