A powerful earthquake in Taiwan felled a 16-storey apartment complex full of families who had gathered for Lunar New Year celebrations Saturday, with at least eleven dead and more than 30 feared trapped.

The death toll was rising in the historic city of Tainan, which bore the brunt of the 6.4-magnitude quake, as rescuers scoured rubble for survivors.

An entire residential complex of four buildings containing almost 100 homes toppled, left on its side with twisted metal girders exposed and clouds of dust rising from the jumbled concrete.

Among the nine people killed when the apartment complex collapsed were a 10-day old baby girl and two other children, the National Fire Agency said.

The other two victims were killed in different parts of the city by falling debris, the agency said.

Officials say they are unsure how many residents may still be inside, but media reports estimated at least 30 could be trapped.

Around 800 troops have been mobilised to help the rescue effort, with sniffer dogs also searching through the rubble.

Residents at the felled 16-storey Wei-kuan Building told of their terror as the quake hit, with survivors pulled bleeding and crying from the ruins, some just in their underwear.

"I saw buildings shake up and down and left and right," said one resident.

"The first and second floor just collapsed," he told local channel SET TV.

Another man tied his clothes together to create a rope and lowered himself from his home on the ninth floor to the sixth floor below, Apple Daily reported.

One woman told how she had fought her way out of her home.

"I used a hammer to break the door of my home which was twisted and locked, and managed to climb out," she told SET TV, weeping as she spoke.

Rescuers have freed more than 250 people from the apartment complex, with over 40 of them hospitalised.

Interior minister Chen Wei-jen said he feared there may be more people in the building than usual as family members would have returned to celebrate the Lunar New Year holidays next week.

"We are concerned that most members of those families may have returned for the coming new year holiday," he said.

Heartfelt appeals for the missing were posted on social media.

"My friend in Wei-kuan is currently missing. His brother is waiting at the scene and other relatives are at the hospital looking among those injured. If anyone has related news, please get in touch," one user called applexgreen posted on Taiwan's popular PTT forum.

Another named Ahan asked for information on a family of three with a two-year-old son who lived on the seventh floor of the building.

"My mother is the child's nanny. We haven't been able to get in contact," the post said.

- Dazed and exhausted -

Officials said there were 256 people registered as living in the complex, which contained 96 apartments.

Dazed and exhausted residents stood outside the toppled buildings, watching rescue workers free survivors -- from infants to the elderly, some strapped to stretchers -- and carefully hand them down ladders.

Cranes towered over the disaster zone with diggers trying to move slabs of concrete.

Eight shelters have been set up around the city, with over 100 people taking refuge there, while restaurants and hotels offered free food and rooms to residents.

"The buildings collapsed, but Tainan will stand again! Please treat here like your temporary home, rest well and freshen up. You aren't alone," said one Tainan hotel called Adagio Travel on its Facebook page.

Separately, at least 30 people were earlier freed from another residential seven-storey tower.

Officials said several blocks had collapsed or half collapsed in other parts of the city, with some buildings left leaning at alarming angles.

Across Tainan, more than 400 people were injured, with over 60 hospitalised.

Around 400,000 had been left without water, authorities said, and more than 2,000 homes are still without electricity.

China has offered rescue assistance if needed, according to state news agency Xinhua.

The quake struck at a depth of 10 kilometres (six miles) at around 4:00 am (2000 GMT Friday), 39 kilometres northeast of Kaohsiung, Taiwan's second-largest city.

Taiwan lies near the junction of two tectonic plates and is regularly hit by earthquakes.

The island's worst quake in recent decades was 7.6 magnitude in September 1999, killing around 2,400 people.