Kono said the government hopes Japanese nationals and companies will not be subjected to detrimental treatment as a result of the ruling, but stopped short of expanding on what kind of actions he believes should be taken.
South Korean President Moon Jae-in had no immediate reaction to the ruling.
If Japanese companies refuse to pay compensation, their assets in South Korea may be seized by authorities, the sources said.
The 94-year-old Lee Chun-sik said it was "heartbreaking" to attend the hearing on his own.
"I'm just very sad that I am the only one remaining", Lee told reporters, teary-eyed and choking. "It would have been good if we were still here altogether". The current company, one of the world's largest steel producers, was formed from the merger of several companies after the war.
Nippon Steel said on Tuesday the ruling was "deeply regrettable" and that it would carefully review the court decision, taking into account the Japanese government's response.
Asked if the art troupe's performance in Seoul could be held in November, the ministry official did not provide a direct answer, only to say that the two Koreas will continue to work on implementing what was agreed upon during the Moon-Kim summit in September. He was speaking after arriving Sunday for meetings with South Korean officials including local counterpart, Lee Do-hoon - their second face-to-face talks in a week.
Japanese courts dismissed the case, saying their right to sue had been extinguished by the 1965 treaty which saw Seoul and Tokyo restore diplomatic relations and included a reparations package of about $800 million in grants and cheap loans.
Japanese Prime Minister Shinzo Abe criticised the South Korean ruling, saying it was "impossible" under global law and that the issue had been "completely and finally settled" by the 1965 treaty.
Seoul, the South Korean capital, remains vulnerable to attack because of the retention of North Korea artillery, Champoux said.
"There are likely more obstacles left before the victims receive compensation", Kim said.
The ruling could fundamentally reverse the legal foundation of friendly and cooperative relations between the two countries, Japan's top envoy warned. "Seizing the companies' assets in South Korea could also be a long and hard process if they continue to refuse paying the victims".
At that time, the court sent back such compensation cases, including Nippon Steel's case, to Seoul High Court.
But the victims - along with two others including Lee - launched a separate action in South Korea in 2005, and in 2012 the Supreme Court in Seoul ruled that the company was liable.
Tuesday's ruling eliminated the "room for diplomacy" and Japan could take the case to worldwide arbitration, though South Korea is not a member of the global Court of Justice, said Jin Chang-soo, a senior fellow at the Sejong Institute think tank south of Seoul.