SEOUL, South Korea — Until recently, few had heard of PNR, a company in South Korea that turns sludge from steel mills into iron. Then a 94-year-old man named Lee Chun-shik tried to settle an old debt.

Mr. Lee grew up during the Japanese occupation of Korea, and as a teenager, he was taken to Japan and forced to work for a steel maker, essentially as slave labor. Today, that steel maker is Japan’s largest, Nippon Steel & Sumitomo Metal, with assets around the world, including $9.6 million worth of shares in PNR.

Mr. Lee asked a court in South Korea to seize some of those shares as compensation for what he endured so long ago — and the court did so last month.

The ruling is now at the center of a bitter dispute that has called into question the foundation of diplomatic ties between America’s top allies in Asia, driving them apart even as Washington is trying to build a united front against China’s rise and a nuclear-armed North Korea.