BEIJING (Reuters) -China's military started two days of "punishment" drills around Taiwan on Thursday in what it said was a response to "separatist acts", just days after new Taiwan President Lai Ching-te took office and called on Beijing to cease its threats.

China detests Lai, saying he is a "separatist", and it has denounced his inauguration speech on Monday. Chinese Foreign Minister Wang Yi this week called Lai "disgraceful".

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

The Eastern Theatre Command of the Chinese People's Liberation Army (PLA) said it had started joint military drills, involving the army, navy, air force and rocket force, in areas around Taiwan at 7:45 a.m. (2345 GMT).

The drills are being conducted in the Taiwan Strait, the north, south and east of Taiwan, as well as areas around the Taiwan-controlled islands of Kinmen, Matsu, Wuqiu and Dongyin, the command said in a statement.

There was no immediate comment from Taiwan's government.

The drills focus on joint sea-air combat-readiness patrols, precision strikes on key targets, and integrated operations inside and outside the island chain to test the "joint real combat capabilities" of the forces, China's military said.

"This is also a strong punishment for the separatist acts of Taiwan independence forces and a stern warning against the interference and provocation by external forces," the command added.

In August 2022, China launched live-fire military exercises around Taiwan immediately after a visit, much condemned by Beijing, by former U.S. House speaker Nancy Pelosi. That series of exercises, the scale of which was unprecedented, lasted for four days, followed by several days of additional drills.

(Reporting by Beijing newsroom; Editing by Christopher Cushing and Gerry Doyle)