They were referring to remarks made by Lee to Natsuo Yamaguchi, leader of Komeito, Abe's ruling Liberal Democratic Party's coalition ally on Wednesday.

Lee reportedly told Yamaguchi that he had hoped the talks with Abe would help create an environment in which the two sides could begin to work towards establishing "future-oriented" ties.

But, nevertheless, despite the highest-level talks being held between both countries in more than a year, Japanese officials intimated after the talks that little progress had been made, and that Japan's expectations remained for South Korea to "change its stance."

Despite the lack of tangible progress made between both sides, with a potential meeting between Abe and Moon on the sidelines of the U.N. General Assembly in New York still up in the air, with Japan asserting its reluctance and stating that the meeting would be conditional, Abe and Lee both agreed in principle that the protracted dispute should not be left unchecked as the two counties are important neighbors.

"At present, bilateral ties are in an extremely severe state, but I believe we should not leave them as they are," the Japanese Foreign Ministry quoted Abe as telling his South Korean counterpart.

Lee, for his part, was quoted by the ministry as saying that he shares an understanding of the importance of dialogue between the two nations.

The pair also agreed that despite the ongoing feud, importance should continue to be placed on people-to-people exchanges between both countries.

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