Peter Dawson, chief executive of the R&A, the St Andrews-based governing body for golf, hit back following claims the ban on female members at the golf club was harming fundraising efforts by the neighbouring university.
However, Louise Richardson, the American principal of St Andrews University, said membership practices that discriminate against women were untenable.
The pair clashed after Ms Richardson spoke about the policy in a US newspaper interview, in which she claimed she had been mocked by members sarcastically waving their club ties at her and felt frustrated to be unable to accompany potential benefactors to lunch at the clubhouse.
However, Mr Dawson sought to dismiss the criticism.
Speaking on the eve of the Open at Royal Liverpool, a club that welcomes women members, he insisted both organisations enjoyed a good relationship.
He said: "To be honest, we just don't recognise those remarks as in any way accurately representing the relationship between the R&A and St Andrews University. We have an excellent relationship.
"We're very supportive of the university. We've been very supportive of its fundraising efforts.
"In fact, its 600th anniversary fundraising has just finished, and we contributed £500,000 to it, a not inconsiderable sum in support of St Andrews University."
He added that he thought "one of two things are not quite as portrayed".
R&A members are due to vote on September 18 on whether to admit women to the club, which is set to host the British Open next year.
First Minister Alex Salmond last year boycotted the tournament at Muirfield. He labelled its men-only membership "indefensible in the 21st century".
Responding to Mr Dawson's comments yesterday, Ms Richarson said: "This should not be about any individual and the R&A, it should be about how, in a time when women increasingly are occupying positions of authority and responsibility, these kind of membership practices are untenable."
Women can dine at the club house as guests of members on occasional Sundays, but speaking to the New York Times Ms Richardson - herself a keen amateur golfer - said she would refuse to eat there until the men-only policy was abolished.
Many of her male predecessors as principal were granted honorary membership of the club but the mother-of-three, 55, has not been offered the privilege five years since she was appointed.
She said the situation had sometimes prevented her from cultivating business relationships in the customary fashion.
Ms Richardson said: "A supporter of the university got in touch and asked if he could possibly have lunch at the R&A today.
"I had to arrange for somebody I know to take him to lunch at the R&A because, of course, I can't.
"I had to arrange for another member of the staff to take his wife to lunch some place in town because, of course, she can't get into the R&A, either."
She also said she often found herself confronted during business meetings by male club members waving their membership ties at her.
She added: "They think that's funny".