BEIJING, Sept 19 (Reuters) - Chinese President Xi Jinping told two US Flying Tigers veterans who fought for China during World War II that China and the US "should and must" achieve peaceful co-existence, offering further cues for both sides to lower persistent tensions.

In his reply to a letter from former pilot Harry Moyer and pilot gunner Mel McMullen, Xi said the people of China and the United States had shared the same enemy in their fight against Japan and had forged a "profound" friendship, according to Chinese state media on Tuesday.

"Looking to the future, China and the United States, as two major countries, bear more important responsibilities for world peace, stability and development," Xi said.

"They should and must achieve mutual respect, peaceful coexistence, and win-win cooperation."

His call for stable and peaceful ties followed a series of meetings and talks between US and Chinese officials in recent months aimed at reducing tensions and restoring channels of communication including contact between their militaries.

The American Volunteer Group, known as the Flying Tigers, was a fighter group, comprising former US pilots hired by the Republic of China led by Chiang Kai-shek's Kuomintang, to fight against Japan in 1941-42.

The airmen, whose planes were iconic for their shark faces, were widely known in China for their feats of bravery in the face of larger Japanese forces as they took to the skies from rural runways paved by Chinese people by hand.

"Currently, China-US relations face many difficulties and challenges," Chinese Vice President Han Zheng told U.S. Secretary of State Antony Blinken on the sidelines of the United Nations General Assembly on Monday.

"The world needs stable and healthy China-US relations," Han said.