Moore, 69, said the women's game "rides on the coat-tails" of the men - a view described as "sexist" by the United States Tennis Association (USTA).
Women's world number one Serena Williams said Moore's statement was "offensive and very inaccurate".
But her male counterpart, Novak Djokovic, claimed his tour should fight for more money.
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Moore said female players "should get down on their knees" in thanks to male counterparts such as Roger Federer and Rafael Nadal. The South African - a former player - later apologised for his "erroneous" remarks.
Tennis legend Martina Navratilova said Moore's comments were "extremely prejudiced", adding female players may boycott Indian Wells if Moore stayed.
Djokovic, who won the BNP Paribas Open at Indian Wells on Sunday, described Moore's remarks as "not politically correct".
But the 28-year-old Serb suggested men should get more prize money because more people watch their matches.
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There has been equal prize money in all four majors - the Australian Open, US Open, French Open and Wimbledon - since 2007, and combined Masters events such as Indian Wells and Miami pay the same to men and women.
In a statement, Indian Wells tournament owner Larry Ellison said: "Ray let me know he has decided to step down from his roles as CEO and tournament director effective immediately. I fully understand his decision."
Speaking in a BBC Radio 5 live special on equality in sport, former badminton world champion Gail Emms said: "If was Novak Djokovic, I would feel aggrieved as well."
The Briton, an Olympic silver medallist, added: "I don't like saying this, but it is easier to be a top female athlete than it is for males, because purely on numbers, how hard you've got to work to get up there.
"I'm not saying the top female athletes don't work hard, and the ones at the top are fantastic athletes and sacrifice and dedicate a lot. It's just a numbers game."
Other arguments so far:

Security was tight, with police sealing off Lahore's biggest Christian neighbourhood and submitting those attending to security checks.
Sunday's bombings of two churches in the Youhanabad area left 17 people dead and more than 70 wounded.
Two days of rioting by Christians followed, with two men lynched.
A reported 5,000 police and paramilitary rangers were deployed on Tuesday to try to prevent further rioting.
The main road into the district was closed with rails and barbed wire.
Shops were also shut as grieving relatives made their way towards burial grounds.
"I would like to tell these terrorists if they think that they can push us back from our faith, they are deadly, entirely, very much at fault," said Manual Mani, a pastor attending the funerals.
The attacks during Sunday mass have been condemned by representatives of all religions in Pakistan.
They also criticised the mob violence that followed, as angry Christian crowds threw stones, blocked roads and lynched two men they accused of being involved in the attack. The family of one of the men has told a Pakistani newspaper that he was an innocent shopkeeper and had not been a militant.
Riot police used tear gas and water cannon to disperse rioters on Monday.
Pakistan's Interior Minister Chaudhry Nisar Ali Khan, speaking at the National Assembly on Tuesday, also condemned the reprisal attacks, saying that they constituted "the worst form of terrorism".
"A similar incident occurred right at the heart of Paris where a synagogue was attacked," Mr Nisar said, "but the minority Jews did not react violently in the French capital."
Christians make up less than 2% of Pakistan's population and many are among its poorest people.
Members of the Christian community say that the riots are a show of anger and frustration from a community that feels unprotected and abandoned by the government.
Indian Wells tournament chief Raymond Moore has quit after his controversial comments about women's tennis.
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Hundreds of Pakistani Christians have attended funerals for the victims of two Taliban suicide bomb attacks in the city of Lahore.