Lai, addressing the crowd outside the presidential office in Taipei on Monday, repeated a call for talks with China, which views the proudly democratic island as its own territory and has never renounced the use of force to bring it under Beijing's control.
"I also want to urge China to stop intimidating Taiwan politically and militarily, and to take on the global responsibility with Taiwan to work hard on maintaining peace and stability across the Taiwan Strait and in the region, to ensure the world is without the fear of war breaking out," he said.
Taiwan President Lai Ching-te and Vice-President Hsiao Bi-khim were inaugurated in Taipei. (AP PHOTO)
"We also want to declare this to the world: Taiwan makes no concessions on democracy and freedom. Peace is the only option and prosperity is our goal for long-term peace and stability."
China's Taiwan Affairs Office said the situation in the Taiwan Strait was "complicated and grim".
"Taiwan independence is incompatible with peace in the Taiwan Strait," it said.
"No matter how the situation on the island changes, no matter who is in power, it will not change the fact that the two sides belong to the same China."
China repeatedly called Lai a "separatist" who risked war in the run-up to his election in January.
Taiwan has faced pressure from China, including regular air force and navy activities near the island, since the election victory by Lai, 64.
Lai, who took over from Tsai Ing-wen after serving as her vice-president for four years, said Taiwan must show its determination to defend itself.
"Fellow citizens, we have the ideal to pursue peace, but we must not have illusions," he said.
"Before China gives up using force to invade Taiwan, citizens must understand this: even if we accept all of China's claims and give up our sovereignty, China's ambition to annex Taiwan will not disappear."
Lai received loud applause after reiterating that the Republic of China - Taiwan's formal name - and the People's Republic of China were "not subordinate to each other", a line Tsai also took.
"We have the ideal to pursue peace, but we must not have illusions," Lai told the crowd. (AP PHOTO)
Attending the ceremony were former US officials dispatched by President Joe Biden, MPs from countries including Japan, Germany and Canada, and leaders from some of the 12 countries that still maintain formal diplomatic ties with Taiwan.
US Secretary of State Antony Blinken congratulated Lai, saying the United States looked forward to working with him "to advance our shared interests and values, deepen our longstanding unofficial relationship, and maintain peace and stability across the Taiwan Strait".
The domestic challenges of Lai and Vice-President Hsiao Bi-khim also loom large, given his Democratic Progressive Party lost its parliamentary majority in January's election.
On Friday, MPs punched, shoved and screamed at each other in a bitter dispute over parliamentary reforms the opposition is pushing.
There could be more fighting on Tuesday when MPs resume discussions.
