The bilateral dispute took a tragic turn earlier on Friday when a South Korean man set himself on fire in front of the Japanese Embassy in Seoul in an apparent protest and later died from his injuries.
A South Korean Foreign Ministry spokesperson said, however, that the date was unilaterally and arbitrarily set by Japan, according to NHK.
The plaintiffs said the laborers were forcibly brought to Japan to work at plants when the Korean Peninsula was under Japanese rule.
The government had proposed that South Korean and Japanese firms create a joint fund to compensate victims of forced labor.
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South Korean courts have said that the individuals involved in the forced labor cases have not been compensated for their pain and suffering.
"What the South Korean government is doing now is equivalent to subverting the post-World War Two worldwide order", Kono said at the beginning of a meeting with Nam.
In his meeting with Ambassador Nam Gwan-pyo at the Foreign Ministry, Kono said Seoul's failure to address the issue violates worldwide law.
"It is extremely problematic that South Korea is one-sidedly leaving alone the situation that violates the global law, which is the foundation of our bilateral relationship", Kono told Nam. "It is bad manners to pretend not to know that".
Jun Iwamatsu, director of the trade control policy division at the Ministry of Economy, Trade and Industry, expressed displeasure Friday evening with South Korea's argument and rejected the possibility of organizing such a meeting.
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Japan has denied that the compensation dispute is behind the export curbs even though one of its ministers cited broken trust with South Korea over the labor dispute in announcing the curbs.
Moon's approval ratings rose 2.9 percentage points from a week earlier on the back of the spread of anti-Japan sentiment and his administration's stern messages over Japan's export curbs, pollster Realmeter said on Thursday.
Japan's foreign minister on Friday summoned South Korea's ambassador and accused Seoul of violating worldwide law by refusing to join in an arbitration panel to settle a dispute over forced labour during the Second World War.
An official at President Moon Jae-in's office denied that South Korea had violated worldwide law, saying that the 1965 treaty didn't cover human rights issues.
In the meantime, the South Korean trade ministry on Friday repeated its demand to hold a meeting by next Wednesday.
Anger over wartime history can stir nationalistic feelings in both countries.
The man in his 70s started a fire inside his vehicle parked in front of the embassy building and later died after being treated in hospital, authorities said, adding around 20 disposable gas canisters were also found in the auto.
The man died in hospital, the official said.
The 78-year-old man's father-in-law was believed to have been be a victim of forced labour by Japanese firms during World War II.
Police and fire officials both declined to comment on the man's possible motivations, citing ongoing investigations.