TAIPEI, Aug 7 (Reuters) - Chinese and Taiwanese warships played high-seas "cat and mouse" on Sunday ahead of the scheduled end of four days of unprecedented Chinese military exercises launched in reaction to a visit to Taiwan by the U.S. house speaker.

Nancy Pelosi's visit last week to the self-ruled island infuriated China, which responded with test launches of ballistic missiles over the island's capital for the first time and the cutting of communication links with the United States.

Some 10 warships each from China and Taiwan sailed at close quarters in the Taiwan Strait, with some Chinese vessels crossing the median line, an unofficial buffer separating the two sides, according to a person with knowledge of the matter.

The island's defence ministry said in a release multiple Chinese military ships, aircraft, and drones were simulating attacks on the island and its navy. It said it had sent aircraft and ships to react "appropriately".

As Chinese forces "pressed" the line, as they did on Saturday, the Taiwan side stayed close to monitor and, where possible, deny the Chinese the ability to cross, the person said.

"The two sides are showing restraint, the person said, describing the manoeuvres as high seas "cat and mouse".

"One side tries to cross, and the other stands in the way and forces them to a more disadvantaged position and eventually return to the other side."

Taiwan said its shore-based anti-ship missiles and its Patriot surface -to-air-missiles were on stand-by.

The Chinese exercises, centred on six locations around the island that China claims as its own, began on Thursday and are scheduled to last until midday on Sunday, the official Xinhua News Agency reported last week.

China's military said on Saturday the sea and air joint exercises, north, southwest and east of Taiwan, had a focus on land-strike and sea-assault capabilities.

Taiwan's defence ministry said on Saturday its forces scrambled jets to warn away 20 Chinese aircraft, including 14 that crossed the median line. It also detected 14 Chinese ships conducting activity around the Taiwan Strait.