President Tsai Ing-wen of Taiwan urged China on Tuesday to seek a peaceful solution to its differences with Taiwan and stressed that the island’s people want to maintain self-rule.

Speaking a day before China’s leader, Xi Jinping, was expected to make a major speech about Taiwan, Ms. Tsai said that China must respect the freedom and democracy of Taiwan’s 23 million people. Her remarks came amid a shift in the island’s political landscape, with Ms. Tsai’s Democratic Progressive Party having suffered major losses in local elections in November. Candidates who favor closer ties with China won mayoral contests in Taiwan’s four largest cities.

“I must emphasize, the results of the past election absolutely do not represent that the will of the people at the grass-roots level seeks to give up our sovereignty,” she said in a New Year’s Day address. Beijing considers Taiwan to be Chinese territory that must be united with the mainland, by force if necessary.

The Chinese government, Ms. Tsai said, “must handle our differences peacefully and as equals.”

That set of differences amounts to one of Asia’s biggest potential flash points. Since Ms. Tsai came to power in 2016, China has ramped up pressure on her government. It has increased patrols by military aircraft, sent bombers to circle the island and sailed an aircraft carrier through the Taiwan Strait.