Osaka mayor Toru Hashimoto issued the apology hours after he was due to meet two former "comfort women", but the elderly South Korean women cancelled over fears of becoming political pawns in a long-running row that has stoked tensions between Tokyo and Seoul.
"It is a shame that I couldn't meet them - I wanted to tell them I am sorry for this misunderstanding," Hashimoto told a press conference.
"I hurt them with my words so it's natural that I want to apologise."
"He has to retract his past comments if he wants to apologise and make us believe it is genuine," supporter Pang Chung-Ja told a hastily arranged press briefing in Osaka.
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She added there were fears the pair could be "politically exploited".
Earlier this month the mayor said wartime sex slavery served a "necessary" role keeping battle-stressed soldiers in line, setting off a volley of criticism from countries under Japan's rule in the 1930s and 1940s as well as from the US.
Hashimoto today said his original remarks were misinterpreted.
"I happen to have used the word 'necessity' but it doesn't mean I personally meant it was necessary," he said.
"I mean that it is a historical truth that soldiers were using women. Was it not necessary for them?"
Sex slavery is a particularly sensitive issue in Korea, a former Japanese colony whose people made up many of the up to 2,00,000 "comfort women" forcibly drafted into brothels for the Japanese military during World War II.
The editorial in the Korean and English versions of the 'Joongang Ilbo' daily on Monday said the 1945 nuclear bombs dropped by US planes, which together killed more than 2,00,000 people, were justified, saying: "God often borrows the hand of a human to punish the evil deeds of men.