BEIJING, May 20 (Reuters) - China said on Thursday (May 20) that a United States warship illegally entered its territorial waters in the South China Sea, the latest salvo in the two nations' dispute over Beijing's territorial claims in the busy waterway.

In a statement, the Chinese military's Southern Theater Command said that the USS Curtis Wilbur entered the waters near the Paracel Islands without permission, adding that its ships and planes followed the US vessel.

It added that China opposed the US action, which violated its sovereignty and undermined regional peace and stability.

The claim comes a day after China accused the US of threatening peace and stability of the Taiwan Strait after the USS Curtis Wilbur sailed through the waterway that separates Taiwan from its giant neighbour.

The US Navy's Seventh Fleet said that the Arleigh Burke-class guided missile destroyer conducted a "routine Taiwan Strait transit" on Tuesday in accordance with international law.

"The ship's transit through the Taiwan Strait demonstrates the US commitment to a free and open Indo-Pacific. The United States military will continue to fly, sail, and operate anywhere international law allows," it said.

A spokesman for China's Eastern Theater Command expressed strong opposition and condemned the move.

"The US actions send the wrong signals to Taiwan independence forces, deliberately disrupting the regional situation and endangering peace and stability across the Taiwan Strait," he said.

China believes Taiwan's democratically elected government is bent on a formal declaration of independence for the island, a red line for Beijing.

Taiwan President Tsai Ing-wen says they are already an independent state called the Republic of China.

Taiwan's Defence Ministry said the US ship had sailed in a southerly direction through the strait and the "situation was as normal".

The US Navy has been conducting such operations every month or so.

The United States, like most countries, has no formal diplomatic ties with Taiwan, but is its most important international backer and a major seller of arms to the island.

Military tension between Taiwan and Beijing have spiked over the past year, with Taipei complaining of China repeatedly sending its air force into Taiwan's air defence zone.

Some of those activities can involve multiple fighters and bombers.

China has said its activities around Taiwan are aimed at protecting China's sovereignty. Taiwan's government has denounced it as attempts at intimidation.