By Ben Blanchard and Yimou Lee

TAIPEI (Reuters) -China's military launched a new round of war games near Taiwan on Monday, saying it was a warning to the "separatist acts of Taiwan independence forces", drawing condemnation from the Taipei and U.S. governments.

Democratically governed Taiwan, which China views as its own territory, had been on alert for more war games since last week's national day speech by President Lai Ching-te, an address Beijing condemned after Lai said China had no right to represent Taiwan even as he offered to cooperate with Beijing.

The Chinese military's Eastern Theatre Command said the "Joint Sword-2024B" drills were taking place in the Taiwan Strait and areas to the north, south and east of Taiwan.

"The drill also serves as a stern warning to the separatist acts of Taiwan independence forces. It is a legitimate and necessary operation for safeguarding state sovereignty and national unity," it said in a statement carried both in Chinese and English.

The command did not state when the drills would end.

It published a map showing nine areas around Taiwan where the drills were taking place - two on the island's east coast, three on the west coast, one to the north and three around Taiwan-controlled islands next to the Chinese coast.

Chinese ships and aircraft are approaching Taiwan in "close proximity from different directions", focusing on sea-air combat-readiness patrols, blockading key ports and areas, assaulting maritime and ground targets and "joint seizure of comprehensive superiority", the command said.

However, it did not announce any live-fire exercises or any no fly areas. In 2022, shortly after then-U.S. House Speaker Nancy Pelosi visited Taiwan, China fired missiles over the island.

In rare operations, China's coast guard circled Taiwan and staged "law enforcement" patrols close to Taiwan's offshore islands, according to Chinese state media.

Taiwan's defence ministry and coast guard said both agencies had dispatched their own forces while officials said Lai's National Security Council met on Monday to discuss the situation.

National Security Council Secretary-General Joseph Wu said China had ignored Lai's message of goodwill.

"Using military force to threaten other countries goes against the basic spirit of the United Nations charter to peacefully resolve disputes," he told reporters in Taipei.

Taiwan's China policy making Mainland Affairs Council said China's latest war games and refusal to renounce the use of force were "blatant provocations" that seriously undermined regional peace and stability.

Taiwan's presidential office said in a statement that China should face up to the fact of the existence the Republic of China - Taiwan's formal name - and respect the people of Taiwan's choice of a free and democratic way of life.

It should "refrain from military provocations that would disrupt the status quo of peace and stability in the region, and threaten Taiwan's democratic freedoms," the statement said.

In Washington, officials from the administration of U.S. President Joe Biden said they were monitoring the drills and there was no justification for them after Lai's "routine" speech.

"We call on the PRC to act with restraint and to avoid any further actions that may undermine peace and stability across the Taiwan Strait and in the broader region, which is essential to regional peace and prosperity and a matter of international concern," State Department spokesperson Matthew Miller said, using the initials for the People's Republic of China, China's official name.

A senior Taiwan security official, speaking to Reuters on condition of anonymity given the sensitivity of the situation, said they believed China was practicing blockading Taiwanese ports to the north and south of the island and international shipping lanes as well as repelling the arrival of foreign forces.

Taiwan on Sunday had reported a Chinese aircraft carrier group sailing to the island's south through the strategic Bashi Channel which separates Taiwan from the Philippines and connects the South China Sea to the Pacific.

Chinese state media has since Thursday run a series of stories and commentaries denouncing Lai's speech, and on Sunday the Eastern Theatre Command released a video saying it was "prepared for battle".

The PLA's Liberation Army Daily newspaper wrote on Monday that "those who play with fire get burned!".

"As long as the 'Taiwan independence' provocations continue, the PLA's actions to defend national sovereignty and territorial integrity will not stop," the paper said.

China held the "Joint Sword-2024A" drills for two days around Taiwan in May shortly after Lai took office, saying they were "punishment" for separatist content in his inauguration speech.

Lai has repeatedly offered talks with China but has been rebuffed. He says only Taiwan's people can decide their future and rejects Beijing's sovereignty claims.

(Reporting by Ben Blanchard and Yimou Lee; Additional reporting Beijing newsroom and Trevor Hunnicutt in Washington; Writing by Greg Torode; Editing by Stephen Coates and Lincoln Feast.)