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"My inappropriate comments caused a big trouble. I am sorry," Mori, 83, said at an Olympic organising committee meeting.
He said the most important thing now was for the Tokyo Olympics to be a success.
His resignation only months before the postponed Summer Games are scheduled to begin will further erode confidence in the organisers' ability to pull off the event during a coronavirus pandemic.
Mori, a former Japanese prime minister, sparked a furore when he said during an Olympic committee meeting earlier this month that women talk too much.
After a global outcry for him to be sacked, he apologised for his comments but refused to step down.
On Thursday, Mori asked the mayor of the Olympic village, 84-year-old Saburo Kawabuchi, to take over the top position, but by Friday public criticism of his hand-picked successor, another older, male, reportedly saw Kawabuchi turn down the job.
Local broadcaster Fuji News Network reported the government would seek to block the nomination of Kawabuchi.
"We can't give the impression that things have changed unless we install a woman or see a generational shift," FNN cited a government source as saying.
The Mori controversy has done "serious reputation damage" to the Tokyo Olympics, said one source involved in the Olympics.
The source, requesting anonymity due to the sensitivity of the matter, said many officials want a woman to replace Mori.
Local media said Olympics Minister Seiko Hashimoto, a woman who has represented Japan in both the summer and winter Olympics, was being considered as a possible candidate.
Prime Minister Yoshihide Suga had asked Mori if there was either a younger or a female candidate to succeed, but Mori recommended Kawabuchi, Kawabuchi said.
Katsunobu Kato, top government spokesman, said he was not aware of Suga's conversation with Mori.