The ministry said Pompeo expressed an "understanding" of South Korea's position and agreed to help facilitate communication through diplomatic channels among Washington, Seoul and Tokyo.
Tokyo last week tightened the approval process for Japanese shipments of photoresists and other sensitive materials to South Korean companies, which need the chemicals to produce semiconductors and display screens used in TVs and smartphones.
The diplomatic dispute over that has further soured relations long troubled over Japan's brutal colonial rule of Korea before the end of World War II.
"(Minister Kang) expressed concern that Japan's trade restrictions would not only inflict damage to our companies, but could also disrupt global supply chains and cause negative effects not only to U.S. companies but also to the global trade order," the ministry said in a press release.
"This would not be ideal for the bilateral friendship and cooperation between South Korea and Japan and also the three-way cooperation between South Korea, the United States and Japan," it said.
Kim Hyun-chong, deputy chief of South Korea's presidential National Security Office, arrived in Washington on Wednesday and told reporters he would discuss the trade spat with Japan with U.S. officials. His trip came a day after South Korean President Moon Jae-in urged Japan to refrain from pushing the situation to a "dead-end street" and respond to Seoul's efforts to resolve the matter diplomatically.
"I came because there are a lot of bilateral issues between South Korea and the United States to be discussed in meetings with the White House and also the Senate and House," Kim told South Korean reporters at Dulles International Airport. When asked whether South Korea would ask the United States to mediate in the trade dispute with Japan, Kim said, "That issue will be discussed too."
The deteriorating relationship between South Korea and Japan could possibly complicate U.S. efforts to strengthen three-way cooperation on North Korea's nuclear program and in countering China's growing influence in the region. But it's unclear whether the Trump administration would be willing to intervene.
South Korea's Ministry of Trade, Industry and Energy said its minister for trade, Yoo Myung-hee, will head for the United States soon to discuss the Japanese trade curbs. South Korean trade officials plan to visit Tokyo to meet with their Japanese counterparts on Friday. So far, Japan has so far shown no willingness to negotiate. It will likely use the meeting to explain and reaffirm its stance, the ministry said.
According to the ministry's figures, Japanese direct investment in South Korea dropped 51% in January-June from a year earlier, to $330 million.
Park Tae-seong, a senior ministry official, said the decline was unrelated to Tokyo's trade curbs. He sidestepped questions of whether antagonisms were hurting investment.
South Korea relies heavily on exports and is the world's biggest supplier of computer chips and displays. It sees the Japanese trade curbs as retaliation for court rulings ordering Japanese firms to compensate aging South Korean plaintiffs for forced labor during World War II.
Japanese officials have suggested South Korea is not trustworthy, hinting at security risks and illegal transfers of sensitive materials to North Korea without citing specific cases.