Moon had stated that while it is "undeniable" that the deal is an official bilateral agreement, the "erroneous knot" with Japan over the "comfort women" issue must be untied by Tokyo apologising to the victims.
"It is a universal principle that bilateral agreements are followed", Mr Abe told reporters in his first public comments since the issue flared up again this week. Though tensions have eased somewhat due to the approaching Winter Olympics in Pyeongchang, he wanted the global community to continue putting "maximum pressure" on North Korea in matters concerning the country's nuclear and missile programs, Abe told journalists before leaving on his trip. The Japan-South Korea deal was a promise between countries.
One of the jumbo jets used by Japanese Prime Minister Shinzo Abe for his foreign trips lost a wing panel during a flight.
In 2015, the two nations had sought to turn a page on history with the "final and irreversible" comfort women pact, under which Tokyo gave an apology and one billion yen (S$12 million) for a foundation set up to support the Korean comfort women who are still alive.
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But it said it would no longer use Japanese money to compensate the survivors. It said it would consult with Japan on what to do with the funds already given by the country. "We want to continue to strongly ask South Korea to do the same".
"Truth and justice are key to resolving the issue, but it is not possible to renegotiate the deal", Mr Moon said on Wednesday. Japan's Chief Cabinet Secretary Yoshihide Suga said his participation in the games would depend on his parliamentary schedule.
But tensions are not likely to deteriorate further, given Japan's reaction was not "stronger" than expected, another expert said. They have demanded the deal be invalidated, saying the government did not consult with them in advance and Japan's apology was not honest.
The agreement was finalised by now-ousted president Park Geun-Hye under pressure from Washington in the face of mounting security threats from North Korea. He has pursued a "two track" approach of separating historical issues from current affairs to build a "future-oriented" relationship with Japan.