UNITED NATIONS, Sept 21 (Reuters) - South Korean President Yoon Suk-yeol and Japanese Prime Minister Fumio Kishida held the first one-on-one talks between their countries' leaders since 2019 on Wednesday and agreed on the need to improve relations by resolving issues of dispute.

The meeting took place in New York on the sidelines of the U.N. General Assembly.

Yoon became president in May and has been keen to improve relations with Tokyo, which have been plagued by disputes stemming from Japan's 1910-45 colonization of the Korean peninsula, at a time when both countries face threats from North Korea. Japan has also stressed the importance of strategic cooperation.

"The two leaders agreed on the need to improve bilateral relations by resolving pending issues, and agreed to instruct their diplomats to accelerate talks between them to that end while also continuing discussions between themselves," Yonhap quoted Yoon's deputy spokesperson, Lee Jae-myoung, as saying.

Lee said the leaders shared serious concerns about North Korea's nuclear program, including its recent law authorizing first use of nuclear weapons and the possibility of a resumption of nuclear testing for the first time since 2017.

Both sides described talks as "informal" and said they lasted 30 minutes.

Japan's Foreign Ministry Press Secretary Hikariko Ono said the two leaders "shared the need to bring back the sound bilateral relationship with the resolution of various issues."

She said they agreed to develop relations "in a future-oriented manner based on the foundation of the friendly and cooperative relationship that both countries built since the normalization of diplomatic relations in 1965."

Yonhap said Yoon and Kishida met several times on the sidelines of the North Atlantic Treaty Organization (NATO) summit in Madrid in June, which included a trilateral meeting with U.S. President Joe Biden, but Wednesday's meeting was the first time they had sat down for one-on-one talks.