TAIPEI, Taiwan — In very different ways on Wednesday, citizens of Taiwan used an important holiday to call for the 23 million people of this self-governing island — which Beijing claims as its territory — to have a greater say in their political identity.

Young protesters in the northern city of Taoyuan, carrying an anti-China banner, splashed red paint on the tomb of Chiang Kai-shek, the generalissimo who fled to Taiwan after losing China’s civil war to the Communists and who declared martial law on the island that lasted until 1987, 12 years after his death.

And at a news conference in Taipei, the capital, two former presidents called for a referendum in April 2019 on whether to replace the Republic of China, which has been the island’s government since 1945, with a Republic of Taiwan — a move that Beijing has warned would lead to war.

Both developments on Wednesday — the 71st anniversary of an uprising that led to a massacre of Taiwanese by Chiang’s soldiers — highlight the challenges that President Tsai Ing-wen faces in dealing with rising pressure from China while trying to keep Taiwan’s pro-independence voters on her side as midterm elections approach.