The two countries have long encountered strained ties over history and trade.
Feuds dating back to Japan's 1910-45 colonial rule of Korea continue to dog bilateral relations, including the issues of Korean laborers forced to work at Japanese firms and women at military brothels during World War II.
The ties further soured after South Korea's Supreme Court ordered a Japanese steelmaker to pay compensation for forced labor in 2018, which prompted Tokyo to impose export curbs on some key high-tech materials.
In a letter delivered to Moon on Saturday, Suga underscored the need for cooperation between the two neighbors, Moon's spokesman Kang Min-seok said.
"Prime Minister Suga, in particular, said he hoped the two countries overcome difficult issues and build a forward-looking relationship," Kang told a briefing.
Moon also sent a congratulatory letter to Suga last week, saying he was willing to sit down anytime to improve relations and foster diplomatic, economic, and people-to-people exchanges.
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