SHANGHAI (Reuters) -China's military began drills around Taiwan on Saturday, saying it was a "serious warning" to separatist forces, in an angry and widely expected response to a visit of Vice President William Lai to the United States.

Lai, the front-runner to be Taiwan's next president at elections in January, returned from the United States on Friday, where he officially made only stopovers on his way to and from Paraguay, though he gave speeches while in the country.

The People's Liberation Army's Eastern Theater Command, which has responsibility for the area around Taiwan, said in a brief statement it was carrying out joint naval and air combat readiness patrols around the island.

It said it was also holding joint exercises and training of naval and air forces, focussing on subjects such as ship-aircraft coordination and seizing control, to test the forces' "actual combat capabilities".

"This is a serious warning against Taiwan independence separatist forces colluding with external forces to provoke," it said.

There was no immediate response from Taiwan's government.

Taiwanese officials had said China was likely to conduct military exercises this week near the island, using Lai's U.S. stopovers as a pretext to intimidate voters ahead of next year's presidential election and make them "fear war".

(Reporting by Casey Hall; Writing by Ben Blanchard; Editing by William Mallard)