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 on Saturday called Lai a "troublemaker" and vowed to take "resolute measures... to safeguard national sovereignty and territorial integrity".

The Eastern Theatre 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" on Saturday, state media outlet Xinhua quoted military spokesperson Shi Yi as saying.

Xinhua said the drills, the scale of which was not immediately known, were meant to test the PLA's ability "to seize control of air and sea spaces" and fight "in real combat conditions".

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

Taiwan on Saturday said it strongly condemned "such irrational and provocative behaviour" and said it would dispatch "appropriate forces" to respond "with practical actions".

"Conducting a military exercise this time under a pretext not only does not help the peace and stability in the Taiwan Strait, but also highlights (China's) militaristic mentality and confirms the hegemonic nature of its military expansion," Taiwan's Ministry of National Defence said in a statement.

- 'New provocative move' -

China claims Taiwan as part of its territory and has pledged to take it one day, by force if necessary.

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.

But on Saturday, an official from the ruling Communist Party's Taiwan Work Office "strongly condemned" Lai's trip, calling it a "new provocative move" by his party, the DPP, "to further collude with the United States", Xinhua said.

"Lai's latest 'stopover'... was a disguise he used to sell out the interests of Taiwan in order to seek gains in the local election through dishonest moves," the official was quoted as saying.

"Lai's deeds have proven that he is an out-and-out troublemaker who will push Taiwan to the dangerous brink of war and bring deep troubles to Taiwan compatriots", the readout continued.

At a lunch in New York during the trip, Lai vowed "to resist annexation" and continue to uphold the core tenets of Tsai's administration.

Lai has been far more outspoken about independence than Tsai, to whom Beijing is already hostile as she refuses to accept its view that Taiwan is a part of China.

The Harvard-educated doctor turned politician has previously described himself as a "pragmatic Taiwan independence worker".