A woman was pulled alive from the rubble of a collapsed building in the southern Taiwan city of Tainan on Monday and another man has been found alive trapped inside more than 48 hours after a deadly earthquake struck, officials said.

The death toll from the quake rose to 35 earlier on Monday, with more than 100 people still missing.

The quake struck at about 4 a.m. on Saturday (20:00 GMT Friday) at the beginning of the Lunar New Year holiday, with almost all the dead found in the toppled Wei-guan Golden Dragon Building in Tainan city.

Rescue efforts are focused on the wreckage of the 17-story building, where 117 people are listed as missing.

Wang Ting-yu, a legislator who represents the area, told reporters the woman, Tsao Wei-ling, was found lying under her dead husband. Their 2-year-old son, who was also killed, was found lying nearby.

Another person has also been located, a man called Li Tsung-tian, Wang said. The man is conscious and talking to rescuers.

Rescuers continued to scramble over the twisted wreck of the building as numbed family members stood around, waiting for news of missing relatives.

Lin Tong-meng said he had been waiting at the site for word of his 11- and 12-year-old nephews, who have yet to be found.

"I came back and forth all yesterday and now I'm here again," Lin said. The boy's mother and father were rescued soon after the quake. Their father also stood nearby, pacing close to the rubble in tears.

Taiwan's government said in a statement 33 of the 35 dead where from the Wei-guan building.

President Ma Ying-jeou is scheduled to visit the disaster zone later on Monday, as is Tsai Ing-wen, who won a presidential election last month.

Chinese President Xi Jinping conveyed condolences to the victims, state news agency Xinhua reported late on Sunday, and repeated Beijing's offer to provide help.

China views self-ruled Taiwan as a wayward province, to be bought under its control by force if necessary.

(Reporting by J.R. Wu; Additional reporting by Megha Rajagopalan in Beijing; Writing byBen Blanchard; Editing by Paul Tait)