The apology, issued to the male head of the woman's opposition party, according to Jiji Press and the Asahi newspaper, came hours after he issued a blog on the importance of improving the low rate of female workplace participation in Japan.
In the post, Abe called for women to "shine" but made no mention of the episode.
Tokyo assemblyman Akihiro Suzuki, 51, yesterday admitted he had yelled "Why don't you get married?" at Ayaka Shiomura, 35, last week when she was speaking in the chamber during a debate on motherhood.
Hours after the apology his office pelted with raw eggs and his Facebook page was flooded with comments critical of his behaviour. He was also vilified on Twitter.
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Shiomura was questioning senior figures in the Tokyo city administration on plans to help current and future mothers when abuse erupted from seats occupied by LDP members.
Suzuki's shout was captured on tape, while some of those in the chamber said they had also heard laughter and taunts such as "Are you not able to have a baby?"
Japan has one of the lowest rates of female workforce participation in the developed world, and most economists agree it badly needs to boost the number of working women.
But a lack of childcare facilities, poor career support and deeply entrenched sexism are blamed for keeping women at home.
Abe has made great play of his desire to level the gender playing field, making numerous speeches on the subject over recent months.