President Lee Myung-Bak of South Korea paid an unprecedented visit to remote islands disputed with Japan, sparking anger in Tokyo which recalled its ambassador from Seoul in protest.
"I don't know when he will go back to South Korea," Koichiro Gemba, the Japanese foreign minister, told reporters in Tokyo on Friday.
Gemba said he would meet the envoy early on Saturday for discussions on the issue including what "other measures" Japan could take.
Lee was making the first-ever visit by a South Korean president to the rocky volcanic outcrops in the Sea of Japan (East Sea), whose ownership has been disputed for decades between South Korea and its former colonial ruler Japan.
The South has stationed a small coastguard detachment since 1954 on the islands known as Dokdo in Korea and Takeshima in Japan.
Gemba also summoned the South's ambassador in Tokyo to make a strong protest.
"I told him I have no understanding of why President Lee visited the islands at this time," said the foreign minister, who had warned earlier in the day that a visit "would have a great impact" on relations.
Osamu Fujimura, the chief cabinet secretary, called the trip "extremely regrettable" at a time when Tokyo was seeking relations with Seoul which looked to the future rather than the past.
Lee's visit came just days before the August 15 anniversary of Japan's World War II surrender, which ended its 35-year rule over Korea.
South Korea last week summoned a senior Japanese diplomat to protest his country's renewed claim to the islands in its latest defence white paper.
Earlier in July it was Tokyo's turn to protest when a South Korean rammed his truck into the main gate of Japan's embassy in Seoul in response to a demonstration in the city by a right-wing Japanese activist.
South Korea has announced it will stage a regular military exercise near the islands in mid-August, reportedly involving some 10 warships, plus F-15K fighter jets and other weaponry.
The South's military increased patrols by warplanes and naval ships around Dokdo before Lee's visit, according to a military official quoted by Yonhap news agency.
Many older Koreans have bitter memories of Japan's brutal colonial rule.
Historical disputes such as Dokdo still mar their relationship, despite close economic ties and a shared concern at North Korea's missile and nuclear programmes.
Seoul is also irked at Tokyo's refusal to compensate elderly Korean women forced into sexual slavery for Japanese troops during World War II.
In June, the South at the last minute shelved the signing of a military information-sharing agreement with Japan following Korean protests.
A South Korean political analyst said Lee's trip was an over-reaction to diplomatic strains and should have been considered more thoroughly.
Strategically, the visit to Dokdo would be one of the strongest actions the president could take, Jin Chang-Soo of the Sejong Institute think-tank said.
"In the long term, considering there will be many problems [between the two countries], I doubt whether this is the right time to play this card," he told the AFP news agency.
With just over six months of his term remaining, Lee's popularity has slumped amid corruption scandals allegedly involving his brother and close aides.
Dokdo covers a total land area of 18.7 hectares. Apart from the coastguards there are two civilian residents, an elderly man and his wife.
It is sited amid rich fishing grounds and Seoul officials say the seabed contains reserves of gas hydrates, although the amount is still unclear.