Ryuji Sonoda, a 39-year-old former judo champion, bowed before the cameras after announcing the decision to step down during a crowed press conference in Tokyo.
"I would like to deeply apologise for causing trouble to all the people concerned with what I have done and said," Sonoda said.
"I think it will be difficult for me to continue being engaged in the training programme any longer. I wish to submit my resignation."
Sonoda was exposed by 15 anonymous letters delivered to the Japanese Olympic Committee (JOC) by some judokas in December.
The women claimed Sonoda, a member of Tokyo's Metropolitan Police Department, slapped them in the face, kicked them and shoved their breasts on several occasions between August 2010 and February 2012.
According to a JOC report, he also told some athletes to "die" and lashed them with bamboo swords similar to those used in the Japanese martial art of kendo.
The athletes reportedly took action against the coach only after the London Olympics because they feared exclusion from the competition as a reprisal.
Senoda's violent methods were first reported to the All Japan Judo Federation in September, but the body decided to retain the coach after issuing a warning to him.
The athletes then directed their complaint to the JOC by mailing the anonymous letters.
However the Olympic body at first ignored the matter, and launched an investigation just after the judoka revealed themselves and lodged a formal complaint.
Also other members of Senoda's staff have been accused of making use of violence during training sessions.
Japan's sports minister Hakubun Shimomura told the JOC to launch a fresh inquiry into the allegations.
The case has triggered widespread indignation and a national debate about the extensive use of violence and corporal punishments in sports.
A few weeks ago the captain of an Osaka high school basketball team killed himself after repeated physical abuse by his coach.
"It is time for Japan to change the idea that use of violence in sports including physical discipline is a valid way of coaching," Shimomura said.
Tokyo is bidding to host the Olympics and Paralympics in 2020.
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