By Larry King

TROON, Scotland (Reuters) - Golf's rulemakers have dismissed Rory McIlroy's claim that the sport lags behind others at the Olympics when it comes to anti-doping but said their discussions about improving the situation were nothing to do with the public.

Doping is something the Royal & Ancient (R&A) takes seriously, because it strikes at the integrity of the sport, Martin Slumbers, the head of the organization, said on the eve of the British Open at Royal Troon.

"And our belief is that we should be, as a sport, at the highest level of standards around anti-doping," Slumbers told a news conference on Wednesday, a day after McIlroy made his remarks.

"And that's something that the tours and ourselves need to, are privately talking about behind closed doors. It's not a matter for public discussion."

Slumbers said the R&A follows the same policy as the European Tour during the week of the Open, and the Tour administers the testing during the championship.

McIlroy, the 2014 British Open champion, said on Tuesday he was tested "four to five times a year, which is very little compared to the rest of the Olympic sports... I think drug testing in golf is still quite far behind some of the other sports."

In his news conference on Tuesday, McIlroy also said he did not feel he was letting golf down by not playing in this year's Rio Olympics, which will include golf for the first time since 1904.

"I didn't get into golf to try and grow the game," he said. "I got into golf to win championships."

Everybody's entitled to an opinion, Slumbers said, but for the R&A, "it's part of our DNA to focus on developing the game."

Slumbers declined to take credit for Troon's recent vote to admit women, although the vote came early in July, less than two months after Muirfield, another traditional Open venue, voted against letting in women - leading the R&A to drop Muirfield as a future Open host.

He also declined to say whether the R&A would keep the Open out of Turnberry, in view of the appetite for controversy of its new owner, U.S. Republican presidential contender Donald Trump.

"Turnberry is, was and is, part of the pool of courses for the Open Championship," Slumbers said. "There are at the moment nine courses and Turnberry is one of those."

But he also said courses had been chosen for the next three Opens, and an announcement was due soon on the two that would follow them. None of those is Turnberry, which last hosted an Open in 2009.

(Editing by Rex Gowar)