US 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 were scheduled to last until midday on Sunday, the official Xinhua News Agency reported last week.

Taiwan's transport ministry said on Sunday afternoon it was gradually lifting restrictions on flights through its airspace, saying notifications for the drills were no longer in effect.

But Taiwan would continue to direct flights and ships away from one of the drill zones, which China has never confirmed, off its east coast until Monday morning, it said.

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

The United States called the exercises an escalation.

"These activities are a significant escalation in China's efforts to change the status quo. They are provocative, irresponsible and raise the risk of miscalculation," a White House spokesperson said.

"They are also at odds with our long-standing goal of maintaining peace and stability across the Taiwan Strait, which is what the world expects."

China says its relations with Taiwan are an internal matter and it reserves the right to bring the island under its control, by force if necessary. Taiwan rejects China's claims saying only Taiwan's people can decide their future.

China has also warned the United States not to "act rashly" and create a greater crisis.

Australian Associated Press