The Japan Golf Council, unaffiliated with the sport's domestic governing body, the Japan Golf Association -- said on Tuesday that it had sent a letter to International Olympic Committee (IOC) President Thomas Bach proposing an alternative venue.
The membership policy "is quite contrary to the spirit of the Olympic Games," said Eiko Ohya, chairwoman of the council.
The Kasumigaseki Country Club, a private club in neighbouring Saitama prefecture, lets women play Monday through Saturday but bars them from becoming full members and from playing on Sundays.
The council has not received a response from the IOC but feels it is making headway after Tokyo Governor Yuriko Koike recently criticised the policy.
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The council wants the venue to be moved to Wakasu Golf Links, a public course on Tokyo Bay located much closer to the Olympic Village.
Beyond the membership issue, the council believes Wakasu would be more cost-effective due to its proximity to central Tokyo and have greater legacy value for the people because it is a public course.
The uproar adds to a list of troubles for Japanese organisers, who had recently been considering moving three other venues because of soaring costs before sticking to their planned locations at a lower price.
In a statement, the Tokyo 2020 organising committee noted that Kasumigaseki had hosted various national competitions, including the 1999 Japan Women's Open, and that it fully met the requirements for hosting Olympic-level golf competitions.
But the committee added that it "would continue studying the club owner's policy on the membership eligibility and responses to the public discussion."
Hiroshi Imaizumi, general manager at the Kasumigaseki Country Club, told Reuters that the club had about 215 female Monday-Saturday members. He said the club was not considering changing its membership system now but would think about it if it were contacted by the IOC.
Several notable country clubs have changed their policies to allow female members in recent years.
In 2014, the Royal and Ancient Golf Club of St Andrews decided to allow women to join after 260 years of exclusion, and Augusta National, home of the U.S. Masters, ended its men-only membership in 2012.
(Editing by Amlan Chakraborty)
