By Ben Blanchard

KUNMING, China (Reuters) - China and the United States wrapped up a three-day humanitarian relief military drill on Friday, looking past simmering tensions over the disputed South China Sea and uncertainty at what Donald Trump's presidency will mean for defense ties.

The exercises, held in the southwestern Chinese city of Kunming, come a month after a U.S. navy destroyer sailed near islands claimed by China in the South China Sea, prompting fury in Beijing which called the moved illegal and provocative.

That patrol, the latest by Washington to challenge Chinese claims in the strategic waterway, capped a tense year for military-to-military ties between the world's two largest economies, which are also at odds over the U.S. decision to base Terminal High Altitude Area Defense (THAAD) anti-missile system battery system in South Korea to defend against North Korea.

China, neighboring North Korea, worries the system's radar will be able to track its own military capabilities.

New concerns loom with Trump's shock election as U.S. president earlier this month, a man who lambasted China on the campaign trail and has suggested Japan and South Korea be allowed to develop nuclear weapons.

But it was all smiles and friendship as Chinese and U.S. soldiers simulated digging out bodies from an earthquake-destroyed building and rescuing people from an overturned boat in a reservoir. 

Liu Xiaowu, army commander of the Chinese southern military region, and General Robert Brown, commanding general of the U.S. Army Pacific, chatted amiably as they oversaw the last day of exercises.

Asked if he was worried Trump's administration could cancel next year's drills, Brown said he was confident that would not happen.

"I would give my best military advice, if asked at the appropriate time in the transition, that these type of military-to-military exchanges are really critical because of that trust they build."

Liu was upbeat too.

"No matter who is president, as long as it's aimed at humanitarian relief to help relieve suffering of those in disaster zones, it will win support."

This is the fourth time China and the United States have conducted such drills since they began in 2013, as the two try to set aside mutual suspicion from the bottom up, rather than just relying on contacts at a more senior level.

"These operations do help to create a mutual understanding between our two militaries," said Jeremy Reynolds, a U.S. army captain based in Hawaii, standing on a pontoon bridge. 

"The execution of the exchange went very well between the Chinese and the American forces."

The exercise involved 134 military personnel from China and 89 from the United States, using helicopters and engineering equipment.

They also conducted tabletop exercises focusing on sharing information and joint decision-making, field maneuvers focusing on evacuation of earthquake victims and search and rescue.

"We had very happy cooperation with the United States. I was really happy," said Chinese army doctor Zhao Yao.

"This was the first time I'd met the U.S. military. The exchange with them has really helped my English."

(Editing by Nick Macfie)