Activists for comfort women erected a statue of a girl which they call a 'peace monument' outside the Japanese embassy in Seoul in 2011. Photo: AFP
Japan and South Korea's foreign ministers are set to discuss the fraught issue of so-called "comfort women", forced to work in Japanese brothels during World War Two.
Up to 200,000 women are estimated to have been sexually enslaved by Japan during the war, many of them Korean.
It has long strained ties, with South Korea demanding stronger apologies from Japan and compensation for victims.
Earlier this year both sides agreed to speed up talks to resolve the row.
Japan's Fumio Kishida arrived in Seoul on Monday to meet his counterpart Yun Byung-Se, in what correspondents say is a significant move after hints that possible compromise solutions were being considered.
Japan is reported to have proposed setting up a government fund to help resolve the issue. South Korean media reported a tussle over the wording of the agreement, while Kyodo News said there was little agreement over the amount of money Japan should pay.
The news agency reported that Tokyo was considering offering more than 100 million yen ($830,000; £550,000) for a fund for former comfort women, but South Korea wants at least 1 billion.
Mr Kishida told reporters as he prepared to fly out of Tokyo's Haneda airport on Monday: "The comfort women issue is a very difficult issue, but I want to make a last-minute adjustment to consider what I can do."
Analysis - Mariko Oi, BBC News
"Comfort women" is one of two major historic issues that have strained Japan's relationships with its neighbours - the other is the Nanjing massacre.
Few in Japan would disagree that the country's Imperial Army had a prostitution corps during the World War Two.
Women were from Japan, Korea, Taiwan, China and other South East Asian nations. The justification of having such a unit was to prevent soldiers from misbehaving.
While South Korea and other countries demanded an apology and compensation, one of the main debates in Japan has been whether they should be called sex slaves and if they were forced to work as prostitutes.
Some argue that they chose to work for the Japanese army lured by high salaries, citing a job advertisement from the wartime. Others say if they were not allowed to leave freely, that is enough to constitute "slavery".
But even if the foreign ministers could come to an agreement, it would no doubt upset certain camps in both Japan and South Korea.
But it is a significant step in which the two governments are trying to move on from the past that has haunted the two nations' relationships for decades.