By Jack Kim

SEOUL (Reuters) - South Korean President Lee Myung-bak is scheduled to visit a set of remote islands on Friday, angering neighbor Japan which also lays claims to territory believed to contain frozen natural gas deposits that could be worth billions of dollars.

South Korea controls the islands with a coast guard presence and plans to beef up maritime research in an area also rich in marine life.

Lee is the first leader of South Korea to make the trip to the islands that have been a persistent irritant in relations between the two countries even after they moved on from Japan's colonial occupation to develop flourishing commercial ties.

Japan swiftly issued a terse warning over islands, known as Takeshima in Japanese and Dokdo in Korean, which lie equidistant between the two mainlands.

"If it's true, that would run counter to Japan's stance on Takeshima and it would be extremely regrettable," Chief Cabinet Secretary Osamu Fujimura said. "We are now already strongly asking South Korea to call off the visit."

Officials in South Korea said the visit would highlight the islands' importance as a natural reserve and was not aimed at stirring up trouble.

"There shouldn't be anything unusual in a national leader visiting a place that is our territory," an official said.

Lee will travel to a larger island called Ulleungdo off the Korean peninsula's east coast, which is not disputed, and make the final leg, weather permitting.

Lee's scheduled stop on the disputed islands was largely overlooked in South Korea, where he is in the final year of a mandatory single five-year term mired in corruption scandals involving former close aides and family members.

(Additional reporting by Tetsushi Kajimoto in Tokyo; Editing by Nick Macfie)