Lai, who took office in May after winning election in January, is detested by China which calls him a "separatist". Beijing claims democratically governed Taiwan as its own territory, a view Lai and his government reject.
Giving a keynote national address outside the presidential office in Taipei, Lai reiterated that the Republic of China - the island's formal name - and the People's Republic of China are "not subordinate to each other".
"On this land, democracy and freedom are growing and thriving. The People's Republic of China has no right to represent Taiwan," he said.
Taiwan's determination to defend its sovereignty, maintain peace in the Taiwan Strait and seek equal and dignified talks with China all remain unchanged, Lai added.
But he also held out an offer of cooperation with China.
"We are willing to work with China on addressing climate change, combating infectious diseases, and maintaining regional security to pursue peace and mutual prosperity for the well-being of the people on the two sides of the Taiwan Strait."
Lai added that he hoped China could live up to the international community's expectations and apply its influence and work with other countries toward ending Russia's invasion of Ukraine and conflicts in the Middle East.
