The issue of "comfort women" - a euphemism for those forced to work in Japanese wartime military brothels - has long plagued Japan-South Korea ties.
Tens of thousands of women - some say as many as 200,000 - from around Asia, were sent to military brothels to service Japanese soldiers.
Many were Korean. Others were from mainland China, the Philippines, Indonesia and Taiwan.
Only 46 survivors are thought to remain in South Korea. Most are in their late 80s or early 90s.
Arguing terminology - Mariko Oi, BBC News
One of the main debates in Japan about "comfort women" has been whether or not they should be called "sex slaves". Some argue that they chose to work for the Japanese army, lured by high salaries, citing a job advertisement from the 1930s.
The justification at the time for having such a unit, was to prevent soldiers from misbehaving. Others say that if the women were not allowed to leave freely, that is enough to constitute slavery.
There was a famous testimony from a late author, Seiji Yoshida, who said he took part in abducting women on Jeju island during the war. But last year, Japan's Asahi newspaper which cited Mr Yoshida, retracted its articles from the 80s and 90s, saying that they have since judged his statement to be fake.
Japan's Prime Minister Shinzo Abe has also previously criticised the left-leaning Asahi's reports, calling them inaccurate.
Japanese Foreign Minister Fumio Kishida said Prime Minister Abe expresses an "apology and repentance from the bottom of his heart", but it is not Tokyo's first.
In 1993, Japan's then chief cabinet secretary Yohei Kono released a statement admitting that the women had been coerced, although it placed some blame on private contractors to the military. It led to compensation being paid from a government-backed but privately paid-for fund, and survivors being given letters of apology.
There have also been less formal apologies by Japanese leaders. And Tokyo has long argued that the 1965 treaty that restored diplomatic ties and provided more than $800m in Japanese financial help, resolved the matter.
But many Koreans have been reluctant to accept the apologies, wanting Japan to admit legal responsibility for the women, and pay compensation directly from the government.
To critics, the 2012 inauguration of conservative Prime Minister Abe confirmed their doubts about Tokyo's sincerity, as he had previously appeared to question whether the women had been coerced by the military, and because he later opened a review into the 1993 admission of responsibility.
Both countries are trade partners and US allies that Washington wants to co-operate to counterbalance an increasingly assertive China, and a nuclear-armed North Korea.
The mood appeared to warm after the two countries' leaders met for the first time in three years, in November.
After that, South Korean courts acquitted a Japanese journalist accused of defaming President Park Geun-hye, and declined to hear a claim for compensation for colonial-era forced labour. At the same time Tokyo's stance has also appeared to soften.
The BBC's Kevin Kim in Seoul says timing was also a factor.
Earlier in 2015, Ms Park called for a resolution to the dispute by the year's end, marking the 50th anniversary of diplomatic relations between the two countries.