HONG KONG — Taiwan’s president delivered a resounding affirmation of its freely elected government on Monday, noting that its deepening foothold on the island stands in stark contrast to the authoritarian government of mainland China.

In her first National Day speech, President Tsai Ing-wen called for talks between Taiwan and the mainland government, but she emphasized that Beijing should acknowledge Taiwan’s choice to become a democracy. China considers Taiwan to be a renegade province, while the self-governing island Ms. Tsai leads traces its roots to the formation of the Republic of China in 1911 that overthrew the last Chinese dynasty, only to lose the Chinese civil war to the Communists in 1949.

“I call upon the authorities of mainland China to face up to the reality that the Republic of China exists, and that the people of Taiwan have an unshakable faith in the democratic system,” Ms. Tsai said.

One of the goals of the Chinese government is to reunify Taiwan with the mainland. Although Beijing has never renounced the use of force against the island, it has offered to achieve unification by giving Taiwan considerable autonomy, similar to an arrangement that paved the way for Hong Kong to be returned to Chinese rule in 1997, after more than 150 years of British control.