BEIJING (Reuters) - A Chinese warship has held exercises with the U.S. navy off Hawaii, domestic media reported on Tuesday, the latest demonstration of warming military ties since their spy plane stand-off in 2001.

The two countries broke off military contacts after a Chinese fighter jet collided with a U.S. surveillance plane, killing the Chinese pilot and forcing the U.S. crew to land in China, where they were held for 11 days.

But Admiral William Fallon, Commander of the U.S. Pacific Command, has pushed to upgrade ties, visiting China in May and inviting Chinese officers to observe U.S. naval exercises in the Western Pacific.

In the latest exercises, near Pearl Harbor, U.S. and Chinese missile-equipped destroyers held five hours of communications and other drills on Sunday, Xinhua news agency said.

The exercises, visits to naval sites in Hawaii and barbecues with the U.S. navy "broadened communication and contact and increased understanding", the report said. The fleet then headed for San Diego.

Despite improved relations, China's military modernization and expanding military budget are a source of friction with the United States.

Washington has called for more transparency and warned that a Chinese military build-up could destabilize Northeast Asia by altering the balance of power in the region.