By Ryan Woo and Ben Blanchard

BEIJING/TAIPEI (Reuters) -China on Sunday condemned a brief U.S. visit by Taiwan Vice President William Lai, saying he was a separatist and "troublemaker through and through" and Beijing would take strong steps to protect its sovereignty, drawing a rebuke from Taipei.

Lai, front-runner to be Taiwan's next president at elections in January, arrived in New York late on Saturday for what is officially a transit on his way to Paraguay for the inauguration of its president.

China, which claims democratically governed Taiwan as its own territory, has repeatedly denounced Lai's trip, which includes another stopover in San Francisco on Wednesday on his way back to Taipei.

In a statement issued shortly after Lai landed in New York on a scheduled flight from Taipei, China's foreign ministry said it opposed any form of visit by "Taiwan independence separatists" to the United States.

"Lai stubbornly adheres to the separatist position of Taiwan independence and is a troublemaker through and through," the ministry said.

Taiwan is the "core of China's core interests" and facts have shown again and again that the reason for the rise in tensions in the Taiwan Strait is Taiwan trying to "rely on the United States to seek independence", it said.

"China is closely following developments and will take resolute and vigorous measures to defend national sovereignty and territorial integrity."

Taiwan's China-policymaking Mainland Affairs Council said China was the real troublemaker, pointing to its standoff this month with the Philippines in the South China Sea and continued military harassment of Taiwan, among other actions.

"Our government firmly defends national sovereignty and security, guards the lines of defence of democracy and freedom, and will never back down, let alone capitulate," the council said in a statement.

China has an especial dislike of Lai, who has previously described himself as a "practical worker for Taiwan independence", though he has repeatedly said on the campaign trail he is not seeking to change the status quo, but that only Taiwan's people can decide their future.

'LOW KEY' VISIT

A person familiar with the trip's planning said Lai will join receptions with overseas Taiwanese during the stopover in New York, during which he will make a speech.

He will not meet U.S. lawmakers, the person said, adding Lai will keep the visit "low key", in line with Taipei and Washington's shared position to "jointly manage risks when facing an authoritarian region at this sensitive time".

Lai, greeted by supporters waving flags as he arrived at his New York hotel, wrote on social media platform X he was "looking forward to seeing friends and attending transit programs in New York".

Laura Rosenberger, chair of the American Institute in Taiwan (AIT), a U.S. government-run non-profit that carries out unofficial relations with Taiwan, said on X that she would meet Lai in San Francisco, where he is due on Wednesday on his way home.

China is likely to launch military drills this week near Taiwan, using Lai's U.S. stopovers as a pretext to intimidate voters ahead of a next year's election and make them "fear war," Taiwanese officials say.

On Sunday, the Eastern Theatre Command of China's People's Liberation Army, which is responsible for the area around Taiwan, posted on its WeChat account a short video of fighter jets practicing dog fights at an undisclosed location.

It said its forces had recently been engaged in "high-intensity flight training".

Lai's transits come as Beijing and Washington are trying to improve relations.

That includes the prospect of a visit to the U.S. by Chinese Foreign Minister Wang Yi, which could pave the way for a meeting between U.S. President Joe Biden and China's leader Xi Jinping this year.

China has stepped up its military activities around Taiwan over the past three years, seeking to force the island into accepting Beijing's sovereignty.

In April, China staged war games around Taiwan in an angry response to Taiwan President Tsai Ing-wen meeting U.S. House Speaker Kevin McCarthy in California on a stopover on the way back to Taipei following her visit to Central America.

(Reporting by Ryan Woo and Ben Blanchard; Additional reporting by Yimou Lee in Taipei and Jeenah Moon in New York; Editing by William Mallard and Jamie Freed)