South Korea temporarily recalled its ambassador from Japan in protest and stepped up security around the islands.
On Tuesday Yu Myung Hwan, South Korea's foreign minister snubbed an offer from his Japanese counterpart to meet on the sidelines of the annual Association of Southeast Asian Nations (Asean) regional security summit in Singapore.
Instead the two men had an "extremely short but very meaningful exchange of views", Masahiko Komura, Japan's foreign minister said.
Following the rejection, Japan's foreign ministry said it hoped the dispute will not undermine the warming of diplomatic ties between the rival nations.
|About 50 South Korean policemen live on the islands [EPA]
"We just hope that the difference between the two governments on this issue will not damage the otherwise solid and cordial bilateral relationship between Japan and the Republic of Korea," said Kazuo Kodama, a spokesman for Japan's foreign ministry.
Kodama said Tokyo was anxious to get cooperative relations back on track and remained committed to lifting ties to an "even higher dimension".
Seoul and Tokyo have long been at odds about who has sovereignty over the rocky outcrops situated about half way between the two countries.
About 50 South Korean policemen live on the islands, which according to a South Korean newspaper, the government has earmarked for building a hotel and permanent village.
Seoul has also found an unlikely ally in North Korea, which aired news saying that Japan's "distortion of history and the 'dominion over Takeshima' is an unpardonable move" seen as a move to re-invade the region.
Japan however chose to take a softer line.
"If military tensions escalate, that would bring no benefit to either Japan or South Korea," Nobutaka Machimura, Japan's chief cabinet secretary. "So we need to calmly deal with the situation."
In April, the two sides held their first full-fledged bilateral summit in three years.
Ties had been suspended after repeated visits by earlier Japanese leaders to a Tokyo shrine honouring the country's war dead including convicted war criminals.