South Korean President Roh Moo-hyun has accused Japan of denying Korean independence, by laying claim to islands midway between the two nations.
President Roh made his comments in a special TV address
In a televised address, President Roh said South Korea would hold on to the isolated rocks whatever the cost.
The islands, known as Dokdo in Korea and Takeshima in Japan, have been a recurring flashpoint in relations.
Soon after Mr Roh's comments, Japanese leader Junichiro Koizumi offered to hold a summit to discuss the dispute.
A potential clash between the two countries was narrowly avoided last week, after Japan threatened to send ships into the disputed waters.
The BBC's Charles Scanlon in Seoul says Japan's increasingly insistent claim to the islands has sparked nationalist fury in South Korea.
President Roh said the uninhabited rocks symbolised the restoration of the country's independence from Japan after World War II.
"We will react strongly and sternly against any physical provocation," Mr Roh said.
"This is a problem that can never be given up or negotiated, no matter at what cost or sacrifice."
He said Japan had seized the islets during a war of aggression, and its claims to sovereignty now showed a desire to take back its former colony and deny Korean independence.
The islands also lie within rich fishing grounds, and it is thought they may allow access to extensive gas fields.
The confrontation has escalated as Japan adopts a more assertive position in the region, our correspondent says.
South Korea mobilised 20 patrol boats last week, to confront a planned incursion by Japanese survey ships.
Emergency talks over the weekend led to a temporary and shaky compromise.
Japan called off its maritime survey after South Korea agreed to drop plans to register new names for trenches and ridges on the seabed.
"We would like to deal with this in a cool-headed manner, putting priority on maintaining Japan-South Korea relations," Japanese Prime Minister Junichiro Koizumi said in response to Mr Roh's comments.
He said he was willing to meet the South Korean leader to talk over their countries' differences.
"I think we should hold a summit. I have always said that I am ready to carry out a summit," he said.
Both allies of the United States, South Korea and Japan have been close economic and diplomatic partners, but our correspondent says the relationship has recently been poisoned by rising nationalist sentiment in both countries.
There is still deep sensitivity in South Korea over the Japan's 1910-45 colonial rule of the Korean Peninsula.