In 2014, when Lai Ching-te was a rising political star in Taiwan, he visited China and was quizzed in public about the most incendiary issue for leaders in Beijing: his party’s stance on the island’s independence.

His polite but firm response, people who know him say, was characteristic of the man who was on Saturday elected president and is now set to lead Taiwan for the next four years.

Mr. Lai was addressing professors at the prestigious Fudan University in Shanghai, an audience whose members, like many mainland Chinese, almost certainly believed that the island of Taiwan belongs to China.

Mr. Lai said that while his Democratic Progressive Party had historically argued for Taiwan’s independence — a position that China opposes — the party also believed that any change in the island’s status had to be decided by all its people. His party was merely reflecting, not dictating, opinion, he said. The party’s position “had been arrived at through a consensus in Taiwanese society,” Mr. Lai said.