Relations between Japan and South Korea are arguably at their lowest ebb since they normalised ties in 1965, with both sides threatening trade actions which could disrupt the global supply of semiconductors..
Japan has already tightened restrictions on some high-tech materials in what is seen as a response to South Korean court rulings ordering Japanese compensation for wartime forced labourers.
A U.S. official said in Washington that the United States has urged both nations to consider signing a "standstill agreement" on their dispute to buy time for them to negotiate.
Pompeo was due to meet the foreign ministers of Japan and South Korea separately and then in a three-way discussion on the sidelines of the Association of Southeast Asian Nations Regional Forum in Bangkok, Thailand.
"We will encourage them to find a path forward," Pompeo told reporters on Tuesday aboard the plane en enroute for Bangkok.
"They're both great partners of ours. They're both working closely with us on our effort to denuclearise North Korea. So if we can help them find a good place for each of the two countries we'll certainly find that important for the United States."
Asked about Pompeo's statement, Japan's Chief Cabinet Secretary Yoshihide Suga said Tokyo has been conveying its stance and thoughts on various issues to the United States.
"We are closely cooperating with the U.S. We will make efforts to gain correct understanding," he told a news conference.
Suga said he was aware of the media report on the "standstill agreement" but said there was "no such fact."
"The relationship between Japan and South Korea has been in a very severe situation because of negative actions by South Korea," he added.
"There is no change to our stance that we continue to urge South Korea to take constructive actions based on our consistent stance over various issues."
A South Korean court ruled last year that Japanese companies had to pay compensation to South Koreans forced to work in Japanese factories during Japan's occupation of the Korean peninsula from 1910 to 1945.
Japan tightened restrictions on exports to South Korea of key high-tech materials in making memory chips and display panels, accusing its neighbour of inadequate management of sensitive items.
But the curbs were also seen as retaliation against last year's ruling by the South Korean Supreme Court. Japan says the court's decisions violate international law because compensation was settled under the 1965 treaty.
South Korea is bracing for Japan's decision to drop it from a "white list" of countries that enjoy minimum trade restrictions, which could come as soon as Friday, Seoul's foreign minister said on Tuesday.