• Lai, who was sworn in on Monday, said in his inaugural address that Taiwan "cannot make any concessions on democracy and freedom."
• Lai took over from his predecessor Tsai Ing-wen, who is stepping down after eight years because of the two-term limit on the presidency.
• China has repeatedly denounced Lai as a "stubborn worker for Taiwan independence" and a dangerous separatist.

Taiwan's new President Lai Ching-te urged China to stop its hostile political and military threats against the island and work toward regional peace.

Lai, who was sworn in on Monday, said in his inaugural address that Taiwan "cannot make any concessions on democracy and freedom."

In his speech, the 64-year-old doctor turned politician urged Beijing to "choose dialogue over confrontation."

Lai took over from his predecessor Tsai Ing-wen, who is stepping down after eight years because of the two-term limit on the presidency.

His vice president, Hsiao Bi-khim, a former de facto Taiwan ambassador to the United States, was also sworn in on Monday.

Lai won January's election that ushered in an unprecedented third presidential term for the Democratic Progressive Party.

China has repeatedly denounced Lai as a "stubborn worker for Taiwan independence" and a dangerous separatist.

Beijing considers democratically governed Taiwan as its own territory and Chinese President Xi Jinping regards reunification with the mainland "a historical inevitability."

"I also want to call on China to cease their political and military intimidation against Taiwan, share with Taiwan the global responsibility of maintaining peace and stability in the Taiwan Strait as well as the greater region, and ensure the world is free from the fear of war," the new leader said.

The Chinese government has yet to issue a statement in response to Lai's inauguration. 

In recent weeks, China has increased military incursions around the island ahead of the Lai's inauguration, according to Reuters.

Chinese military forces have been getting closer to the Taiwanese shores, said Raymond Kuo, director of the Taiwan Policy Initiative at the RAND Corporation, warning that "there's a much greater chance of escalation and miscalculation."

According to Kuo, ''this is very much driven by the Chinese side. They are the ones who are pushing... where the red line actually is," he told CNBC's "Squawk Box Asia" on Monday, ahead of Lai's inauguration.

He claimed there would be "much more peace across the strait" if China backs off.

U.S. Secretary of State Antony Blinken congratulated Lai, saying he looked forward to working with him and across Taiwan's political spectrum "to advance our shared interests and values, deepen our longstanding unofficial relationship."

Taiwan has been a thorny issue for Beijing's complex relationship with Washington. The U.S. does not support Taiwan independence but has called for cross-strait differences to be resolved peacefully, "in a manner that is acceptable to the people on both sides of the Strait."

Xi told his U.S. counterpart Joe Biden on the sidelines of the APEC leaders summit in November that Taiwan has always been the "most important and sensitive" issue in China-U.S. relations.

On Monday, China's Commerce Ministry announced sanctions against several U.S. companies involved in arms sales to Taiwan.

Taiwan's constitution makes it clear that the Republic of China — Taiwan's formal name — and the People's Republic of China "are not subordinate to each other," Lai said in his speech.

"All our political parties ought to oppose annexation and protect sovereignty," he added. "And no one should entertain the idea of giving up our national sovereignty in exchange for political power."