His comments came the day after a deadline set by Tokyo for Seoul to name an arbitrator for the dispute.
Japanese Foreign Minister Taro Kono summoned South Korea's ambassador on Friday in a deepening diplomatic row over compensation for Korean wartime forced labour that threatens global supply of memory chips and display screens.
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.
The forced labor issue was thrust to centrestage a year ago when a South Korean court ordered two Japanese firms to pay compensation to Koreans forced to work for them.
Japan's official position regarding its former colony maintain that a 1965 agreement resolved the issue of damages.
South Korea has rejected the Japanese claims and proposed an inquiry by the United Nations Security Council or another global body on the export controls of both countries.
The dispute has triggered a trade dispute, with Japan imposing export bans on South Korea, and some South Koreans boycotting Japanese products.
An elderly South Korean man has died hours after setting himself on fire outside the Japanese embassy in Seoul, police said, at a time of worsening ties between the east Asian neighbours. "To bring it up again as though unaware of what we have said is extremely discourteous".
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.
South Korea offered no answer Thursday to Japan's call to settle the row over Tokyo's wartime forced labor through third-country arbitration, raising tensions further between the neighbors, with both countries turning down resolution proposals from the other.
Seoul's defense ministry said Friday that Seoul's current stance is to keep the GSOMIA, and that it is looking at the pact from the standpoint of "its utility and security cooperation" with Tokyo.
When trade officials from the two countries met in Tokyo last week, Seoul urged Tokyo to agree to another meeting, according to the South Korean side.
"The United States fully supports the ROK-Japan GSOMIA, which demonstrates the maturity of the bilateral defense relationship and improves our ability to coordinate trilaterally".
According to police, he ignited a fire inside his vehicle parked in front of the building where the Japanese Embassy is located.
Meanwhile, in an apparent retaliation on July 4, Japan restricted exports of high-tech items to South Korea.
The move triggered anger in Seoul, but also raised worldwide concern about the effect on the global tech supply chain and the possibility of price hikes for consumers.
Meanwhile, the plaintiffs in the South Korean lawsuits are pushing ahead with procedures to sell off the seized assets of the Japanese companies held in South Korea.