Two people were killed and 42 injured when three buildings collapsed in earthquakes that shook southern Taiwan, authorities said on Wednesday.

The two dead were caught in the collapse of a furniture factory in the southern city of Hengchun, where eight people, including four children, were trapped for a time, the National Fire Agency said in a statement.

While a tsunami warning came to nothing, the quake damaged at least six undersea telecommunication cables, affecting users in Taiwan and South Korea, and was felt in China and Hong Kong.

The biggest quake, measured by Taiwan's Central Weather Bureau at magnitude 6.7 and at magnitude 7.1 by the U.S. Geological Survey, struck off the island's southern coast at 8:26 p.m. (1226 GMT) on Tuesday -- the second anniversary of a massive earthquake and tsunami that left more than 230,000 people in Asia either dead or missing.

Further quakes through the evening in Taiwan were measured at up to magnitude 7.0 by the U.S. agency.

KT Corp., South Korea's top fixed-line and broadband service provider, said in a statement that some of its international lines were affected by the quake.

"(Six) submarine cables are not working due to the earthquake near Taiwan. We are making best efforts to restore the service in a speedy manner," the company said in a statement to Reuters.

An official from Chunghwa Telecom, Taiwan's largest telecoms operator, said none of its lines were disrupted but some businesses reported problems on Wednesday morning.