This Nov 1 story was recast on Nov 2 to include Xi's joke about a backdoor

GYEONGJU, South Korea/BEIJING, Nov 1 (Reuters) - Chinese President Xi Jinping gifted South Korea's President Lee Jae Myung a pair of Xiaomi smartphones and jokingly urged him to "check if there's a backdoor," during a state visit on Saturday that capped the Asia-Pacific Economic Cooperation (APEC) forum.

Lee hosted Xi at a state summit and dinner after the APEC leaders' meeting in the South Korean city of Gyeongju, marking Xi's first visit to the U.S. ally in 11 years.

The choice of the gift - China-made Xiaomi 1810.HK devices brought to the home country of smartphone giant Samsung Electronics 005930.KS - underscored Xi's technological ambitions, recently reinforced in China's economic development plan for the next five years.

After Lee presented Xi with "the finest" wooden board for ancient strategy game Go, the pair walked over to the smartphones wrapped in black boxes and an official noted the displays on the devices were made in South Korea.

Lee lifted one of the boxes and looked at it. He then asked Xi: "How is the communication security?", upon which Xi and other gathered officials erupted in laughter. Xi then pointed at the phones and responded: "You can check if there's a backdoor."

A backdoor risk refers to a hidden method of bypassing normal authentication or security controls.

Both leaders laughed and Lee clapped his hands as they proceeded with the presentation of gifts, which also included a traditional Korean mother-of-pearl inlay lacquered tray.

Xi's comment harkened back to concerns expressed by China over a U.S. proposal for advanced chips sold abroad to be equipped with tracking and positioning functions that prompted U.S. chipmaker Nvidia NVDA.O to say its chips had no "backdoors".

China's foreign ministry and Xiaomi did not immediately respond to Reuters' requests for comment on the exchange. Lee's office said it had no separate comment on Xi's gifts.

At the summit, Lee sought Xi's help in efforts to resume talks with nuclear-armed neighbour North Korea, while Xi told Lee he was willing to widen cooperation and jointly tackle the challenges they face.

In other recent off-the-cuff remarks by Xi, a hot mic caught the Chinese leader and Russian President Vladimir Putin discussing organ transplants and the possibility that humans could live to 150 years at a military parade in Beijing in September.

(Reporting by Joyce Lee and Ed Davies in South Korea and Antoni Slodkowski and Xiuhao Chen in Beijing; Editing by Mark Potter and Jamie Freed)

((joyce.lee@tr.com;))