Lee paid a surprise August 10 visit to the Seoul-controlled islands, known as Dokdo in Korean and Takeshima in Japan.
Japan on Thursday refused to take back a letter sent by its own prime minister after Seoul said it would not accept delivery of the note, as a row over islands threatened to descend into diplomatic farce.
It was the latest move in an increasingly bitter tit-for-tat dispute that has engulfed two of Asia's largest economies for nearly two weeks.
South Korea said earlier in the day it would return the protest from Yoshihiko Noda without answering it, for fear any move to acknowledge the missive would bolster Tokyo's claim to islands that both sides say they own.
That sparked an angry response from Tokyo, which accused its neighbour of contravening diplomatic norms.
"Under usual protocol, it is inconceivable that letters exchanged between leaders are sent back," Chief Cabinet Secretary Osamu Fujimura, the government's top spokesman, told a news conference.
"I hope (South Korean President Lee Myung-Bak) will accept the letter, which was sent to deliver our prime minister's thoughts."
The letter to Lee has not even made it to Seoul, having been kept at the South's embassy in Tokyo, foreign ministry spokesman Cho Tai-Young said, announcing the intention to hand the note back.
But in what was beginning to look like a real live game of hot potato, the Japanese foreign ministry turned away a South Korean diplomat, believed to have been carrying Noda's letter, at the gate of the ministry building, NHK footage showed.
"I'm sorry to say this, but returning a diplomatic letter is below even being childish," Senior Vice Foreign Minister Tsuyoshi Yamaguchi said at a press conference.
The letter was subsequently put in the post, registered delivery, a spokesman at the foreign ministry in Seoul said.
Despite their strong economic ties, the two countries have a frequently uneasy relationship, in which historical animosities constantly play in the background.
That relationship has sharply worsened since Lee paid a surprise August 10 visit to the Seoul-controlled islands, known as Dokdo in Korean and Takeshima in Japan.
(Read by Brian Salter. Brian Salter is a journalist at the China Daily Website.)
