The Alliance Defending Freedom International (ADF) is calling on the International Olympic Committee to protect female athletes.
The IOC has come under fresh pressure over its policies after a controversial boxing match between Italy's Angela Carini and Algerian Imane Khelif ended after just 46 seconds.
Khelif was disqualified from the women's boxing world championships last year after failing testosterone and gender eligibility tests but was permitted to compete in the Olympics.
Karini, 25, broke down in tears after she decided to abandon the fight.
"I am heartbroken. I went into the ring to honour my father. I was told a lot of times that I was a warrior but I preferred to stop for my health. I have never felt a punch like this," she said in a post-fight interview.
"I got into the ring and did my duty as a boxer and tried to fight irrespective of any controversy or anything else. I wanted to win. After the second blow to the nose, I couldn't breathe anymore. I went to my coach and said 'enough' because it takes maturity and courage to stop. I didn't feel like fighting anymore."
ADF president Kristen Waggoner said Thursday's events were "disgraceful".
"How many women's records and bodies must be broken for institutions to stand up for women?" she tweeted.
Many high profile figures have weighed in on the decision to allow the fight.
Reem Alsalem, the UN Special rapporteur on violence against women and girls, tweeted: "Angela Carini rightly followed her instincts and prioritized her physical safety, but she and other female athletes should not have been exposed to this physical and psychological violence based on their sex."
Italian Prime Minister Giorgia Meloni said: "I think that athletes who have male genetic characteristics should not be admitted to women's competitions. And not because you want to discriminate against someone, but to protect the right of female athletes to be able to compete on equal terms.
"I was emotional yesterday when she wrote 'I will fight' because the dedication, the head, the character, surely also play a role in these things. But then it also matters to be able to compete on equal grounds and from my point of view it was not an even contest."
