Suga was speaking to reporters on Friday.
He referred to a meeting between Japanese Foreign Minister Taro Kono and his South Korean counterpart Kang Kyung-wha in France on Thursday. He said Kono urged South Korea to take concrete action immediately to settle the issue in a responsible manner.
Suga declined to disclose details about how South Korea reacted. But he added that so far the country has yet to agree to setting up an arbitration panel over the matter.
Suga said the South Korean government is obliged to agree to arbitration based on a 1965 bilateral agreement.
It stipulates that if any disputes regarding its interpretation and implementation are not resolved through bilateral discussions, they must be referred to an arbitration committee that includes a third country.
Last year, South Korea’s Supreme Court ordered Japanese companies to pay damages to those who say they or their relatives were forced to work for the firms during World War Two.
But Tokyo says the issue of the right to claim compensation was settled completely and finally under the 1965 bilateral agreement.