CHENGDU, China—Japan’s leader blamed South Korea’s president for the poor state of relations between the two U.S. allies, setting a chilly tone at their first formal meeting in more than a year.

Prime Minister Shinzo Abe and President Moon Jae-in last sat down for official talks in September 2018, but since then a series of disputes has brought their relations to a new low. South Korea’s Supreme Court late last year ordered Japanese companies to financially compensate Koreans forced to work in Japanese factories during World...