BEIJING, Aug 13 (Reuters) - China's foreign ministry on Sunday condemned a brief U.S. visit by Taiwan Vice President William Lai, saying he is a separatist and "troublemaker through and through" and Beijing will take strong steps to protect its sovereignty.

Lai, front-runner to be Taiwan's next president at elections in January, arrived in New York late Saturday on 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."

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.

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.