China and Japan should reaffirm their "strategic relationship of mutual benefit and give it new meaning", he added.
In brief remarks at the start of the meeting, Kishida told Xi: "Japan and China coexist and prosper as neighbors and have a responsibility to contribute to world peace and prosperity."
Kishida also met Biden at the summit where they discussed issues including "common challenges" that they share with China.
China's push to reaffirm relations with Japan could be partly driven by Tokyo's close ties with its arch-rival Washington, said Rumi Aoyama, an expert on Japan-China relations.
On the sidelines of the APEC summit, Kishida has also met South Korean President Yoon Suk Yeol in their seventh meeting this year.
Persons:
Noushad Thekkayil, Xi Jinping, Fumio Kishida, Xi, Kishida, Joe Biden, Biden, Washington, Rumi Aoyama, Aoyama, Yoon Suk, Yoon
Organizations:
Asian, Hangzhou, Olympic Sports Centre, Getty Images, Japanese, APEC, China, ., Waseda Institute of Contemporary Chinese, South, Economic Cooperation
Locations:
Japan, Aichi, Nagoya, Hangzhou, China's, Zhejiang, San Francisco, China, Taiwan, Beijing, Gaza, U.S, United States, Asia