US President Donald Trump said he is not worried about Beijing's military drills around Taiwan, choosing to instead highlight his rapport with his Chinese counterpart Xi Jinping.

"I have a great relationship with President Xi, and he hasn't told me anything about [the drills]. I certainly have seen it," Trump told reporters at a press conference on Monday.

"No, nothing worries me. They've been doing naval exercises for 20 years in that area," he said.

The two-day war games kicked off on Monday - nearly two weeks after the US announced one of its largest-ever arms sale to Taiwan. The sale had angered Beijing, which sees the self-governed island as a breakaway province.

China's military exercises on Tuesday will see it run 10 hours of live-firing exercises in the sea and airspace of five locations surrounding the island.