BEIJING, April 4 (Reuters) - China warned U.S. House Speaker Kevin McCarthy on Tuesday not to "repeat disastrous past mistakes" and meet Taiwan President Tsai Ing-wen, saying it would not help regional peace and stability, but only unite the Chinese people behind a common enemy.

The Republican McCarthy, the third most senior U.S. leader after the president and vice president, will host a meeting in California on Wednesday with Tsai, during a sensitive stopover in the U.S. that has prompted Chinese threats of retaliation.

China, which claims Taiwan as its own territory, staged war games around the island last August after then-Speaker Nancy Pelosi, a Democrat, visited the capital, Taipei.

Tsai will make what is formally called a "transit" in Los Angeles on her way back to Taipei after a trip to Central America. The U.S. says such stopovers are common practice and there is no need for China to overreact.

But China's consulate in Los Angeles said it was "false" to claim it as a transit, adding that Tsai was engaging in official exchanges to "put on a political show".

No matter in what capacity McCarthy meets Tsai, the gesture would greatly harm the feelings of the Chinese people, send a serious wrong signal to Taiwan separatist forces, and affect the political foundation of Sino-U.S. ties, it said in a statement.

"It is not conducive to regional peace, security nor stability, and is not in the common interests of the people of China and the United States," the consulate added.

McCarthy is ignoring the lessons from the mistakes of his predecessor, it said, in a veiled reference to Pelosi's Taipei visit, and is insisting on playing the "Taiwan card".

"He will undoubtedly repeat disastrous past mistakes and further damage Sino-U.S. relations. It will only strengthen the Chinese people's strong will and determination to share a common enemy and support national unity."

China will closely follow developments and resolutely and vigorously defend its sovereignty and territorial integrity, the consulate added, without giving details.

In a statement on Tuesday, Taiwan's foreign ministry said China had no right to complain, as the People's Republic of China has never ruled the island.

China's recent criticism of Tsai's trip "has become increasingly absurd", it added.

"Even if the authoritarian government continues with its expansion and intensifies coercion, Taiwan will not back down."