BEIJING (Reuters) - China's military started its second day of war games around Taiwan on Friday, with drills to test their ability to "seize power" and control key areas, exercises it has said were launched to punish Taiwan's President Lai Ching-te.

The two days of drills in the Taiwan Strait and around groups of Taiwan-controlled islands near the Chinese coast started just three days after Lai took office.

China, which views democratically governed Taiwan as its own territory and denounces Lai as a "separatist", decried his inauguration speech on Monday, in which he urged Beijing to stop its threats and said the two sides of the strait were "not subordinate to each other".

The Eastern Theatre Command of the People's Liberation Army said in a brief statement that its forces on Friday continued with their drills, dubbed "Joint Sword - 2024A".

The exercises are to "test the ability to jointly seize power, launch joint attacks and occupy key areas", it said.

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 Bernard Orr; Writing by Ben Blanchard; Editing by Christopher Cushing and Gerry Doyle)