By Fabian Hamacher and Yimou Lee

TAOYUAN, Taiwan (Reuters) -Taiwan Vice President William Lai returned on Friday from a sensitive visit to the United States, a trip China has condemned and which has brought warnings from Taiwanese officials it could prompt more Chinese military drills near the island.

"Because of everyone's hard work, Taiwan's power is stronger and stronger, and it showed the international community that Taiwan is a force for good, that the international community really pays great attention to Taiwan," he said after returning to Taiwan's main international airport at Taoyuan.

China claims Taiwan as its territory and has denounced the transit stops in the U.S., calling Lai a separatist and a "troublemaker".

Taiwanese officials have said China is likely to conduct military exercises this week near the island, using Lai's U.S. stopovers as a pretext to intimidate voters ahead of next year's presidential election and make them "fear war".

Democratically governed Taiwan has so far not reported any unusual Chinese military movements near the island.

However, on Thursday Japan's government reported 11 Chinese and Russian naval ships, including destroyers, had crossed waters between the southern Japanese islands of Okinawa and Miyako, a waterway crucial to access to the Pacific and East China Seas.

The islands lie directly to the east of Taiwan and Okinawa is home to a major U.S. military base.

A person familiar with security planning in the region told Reuters the China-Russian fleet had conducted simulation attacks on U.S. forces stationed in Okinawa as well as drills to seize strategic locations.

The U.S. Ronald Reagan carrier strike group was also in the waters about 800 nautical miles (1,500 km) off Taiwan's eastern coast as of Thursday evening, the person added.

A spokesperson at Japan's Joint Staff Office said it was not aware of any such simulations by the Chinese and Russian fleets.

"They have not intruded into Japan's territorial waters and we have not confirmed any dangerous behaviour," the spokesperson said.

"We have offered through diplomatic channels that the repeated joint actions of Chinese and Russian forces in the sea and airspace around Japan are a serious concern from a security perspective."

Russia's defence ministry said on Friday that the Russian and Chinese ships "conducted anti-submarine drills, repelled an air raid by a mock enemy, trained for rescue operations at sea, and mastered skills for take offs and landings on decks of war ships".

The U.S. Navy's 7th Fleet did not immediately respond to a request for comment, and neither did China's Taiwan Affairs Office nor the Chinese defence ministry.

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On Friday, the Taiwan defence ministry's official news agency put out a slickly produced publicity video showing fighters jets taking off and missiles being readied.

"Nobody can encroach on our sovereignty," reads an accompanying caption for the video entitled "The military of the Republic of China is duty-bound to maintain regional peace and stability", referring to Taiwan's formal name.

Lai officially only made transits in the United States, first in New York and then in San Francisco, on his way to and from Paraguay to attend the new president's inauguration in one of only 13 countries that maintains formal ties with Taipei.

While in the United States, he gave speeches to the Taiwanese community and met officials from the American Institute in Taiwan (AIT), a U.S. government-run non-profit that handles unofficial relations.

Lai is frontrunner to be Taiwan's next president at elections set for January. President Tsai Ing-wen cannot run again after two terms.

China especially dislikes Lai because of comments he has previously made about being a "practical worker for Taiwan independence", though he has pledged on the campaign trail to maintain the status quo and offered talks with Beijing.

Speaking after stepping off his flight, Lai made only passing mention of his U.S. stopovers, concentrating instead on Paraguay and pledges of support he received there.

"Thank you for your contributions to the country and to society," he said, "allowing Taiwan to very progressively, self confidently and respectfully go into the international community, and winning the support of the international community."

(Reporting by Fabian Hamacher and Yimou Lee; Additional reporting by Chang-ran Kim and Nobuhiro Kubo in Tokyo; Writing by Ben Blanchard; Editing by David Gregorio and Lincoln Feast)