The special envoy dispatched by South Korea's new President Moon Jae-In said in Tokyo that Seoul wants regular summits and improved relations, which have been hindered by the memory of Japan's harsh colonial rule of the Korean peninsula from 1910-1945.
Abe also struck a conciliatory note, saying: "With the new president, I wish to build future-oriented Japan-South Korea relations."
In what both governments hoped was a major step forward, the two countries had agreed in 2015 to a deal designed to end a row over Korean "comfort women" forced into sex slavery for Japanese soldiers during the World War II.
Moon in a phone call with Abe last week said that most Koreans cannot accept the agreement.
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That raised worries in Tokyo that the issue could again hinder ties, at a time when both countries are seeking unity to face the threat posed by North Korea's nuclear and missile development.
As part of the accord, Japan offered an apology and a payment totalling one billion yen ($9 million) to the dozens of remaining survivers.
Speaking to reporters after Thursday's meeting, envoy Moon Hee-Sang confirmed that the "comfort women" issue had been raised, but did not offer further details.
"We had a serious discussion but I find it uncomfortable to say more about it," Moon said, adding that both sides expressed their positions.
Japan has pressed Seoul to implement the deal and also to remove another "comfort women" statue near the Japanese embassy in Seoul.