Lai, who is the frontrunner in Taiwan's presidential election next year, stopped in New York and returned via San Francisco on a trip to Paraguay, one of a dwindling number of nations that diplomatically recognise Taipei.

China has called Lai a "troublemaker" and vowed to take "resolute and forceful measures to safeguard national sovereignty".

On Saturday, the Eastern Theater Command of the Chinese People's Liberation Army "launched joint air and sea patrols and military exercises of the navy and air force around the island of Taiwan", state media outlet Xinhua quoted military spokesperson Shi Yi as saying.

Xinhua said the drills were meant to test the PLA's ability "to seize control of air and sea spaces" and fight "in real combat conditions".

They also were intended to serve as "a stern warning to the collusion of 'Taiwan independence' separatists with foreign elements and their provocations", it added.

China claims Taiwan and has not ruled out using force to seize it.

It launched major military exercises after Nancy Pelosi, then House speaker, visited Taiwan last year and later when President Tsai Ing-wen met top US lawmakers as she transited through the United States.

Washington had called for calm over Lai's transit, describing the travel as routine.