The dinner, at the presidential Blue House compound next to a former royal palace, includes a beef rib dish accompanied by a gravy made with an "exquisite, 360-year-old soy sauce", said a spokesman for Seoul's presidential office.
The age implies it was made in 1657, the year the father of the US Declaration of Independence signatory Benjamin Franklin was born.
Fermented food including soy sauce is a staple in South Korean cuisine, with soy sauces made by famous artisans and fermented for decades -- or centuries -- sold for tens of thousands of dollars per litre.
Today's menu also includes a grilled sole, known to be Trump's favourite fish. An unnamed official told the South's Yonhap news agency: "The menu contains food that has local, traditional flavour that could also appeal to the taste of the US head of state."
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But it is a marked contrast to the largely familiar US- style fare the president was offered by Prime Minister Shinzo Abe in Japan, with whom he has a significantly warmer relationship than with South Korean President Moon Jae-In.
The Seoul meal also features a prawn that Moon's office said was caught near a disputed island claimed both by the South and Japan.
The Seoul-controlled island off the east coast -- called Dokdo in Korea and Takeshima in Japan -- is at the heart of a decades-long territorial dispute between the two countries, both of them US allies who are confronted by the threat of nuclear-armed North Korea.
And in another diplomatic jab at Tokyo, Moon's office invited Lee Yong-Soo, a former wartime sex slave for Japanese soldiers, to the state dinner.
Japan's Chief Cabinet Secretary Yoshihide Suga said in Tokyo he would not comment on how another country welcomes a VIP.
But Suga cast doubt on whether it was a good idea to use a prawn caught near a disputed island at a time when Japan and South Korea should unite to tackle North Korean issues.