The International Olympic Committee has been forced to issue a correction after its president, Thomas Bach, got in a muddle when defending a decision to let an Algerian boxer who failed a gender test fight in the Paris Games.

In a sign of the issue’s complexity, Bach confused the terms transgender and DSD, an abbreviation of “differences in sexual development”, as he sought to quell the row over a swiftly terminated bout between the Algerian fighter Imane Khelif and the Italian Angela Carini.

“I will not confuse the two issues,” Bach said, before confusing the two issues. He said: “We are not talking about the transgender issue here. This is about a woman taking part in a woman’s category and for all the rest.

“The IOC framework, which is scientifically based, applies to all federations. This is available to everybody on the website and the rules of the international federations are on the websites to be followed by everybody. But I repeat here this is not a DSD case.” The IOC subsequently tweeted that Bach had meant to explain that this was not a transgender case.

Differences of sex development (DSD) describes a group of conditions that occur early in pregnancy in which sex development is not typical. It was previously known as “intersex”. Some people with DSDs are raised as female but have XY sex chromosomes and blood testosterone levels in the male range.

The term transgender refers to people whose gender identity or way of expressing their gender differs from the sex they were registered with at birth.

While the IBA said the two boxers at the centre of the storm, Khelif and Lin Yu Ting of Chinese Taipei, had failed gender eligibility tests in March last year, the IOC on Friday discredited the test before Bach further muddied the waters. The gender eligibility of the two boxers remains unclear.

On Thursday, Carini broke down in tears after she abandoned her bout against Khelif after 46 seconds, saying: “I have never felt a punch like this.”

Khelif competed at Tokyo 2020 but was disqualified from last year’s world championships by the International Boxing Association (IBA) for failing to meet their gender eligibility criteria. Lin also failed the test and is competing at the Paris Games.

A complication is that the IBA has since been stripped of its status as boxing’s governing body over governance issues and has been accused by the IOC of making decisions over gender “arbitrarily”.

On Saturday, Italy’s far-right prime minister, Giorgia Meloni, raised the issue as one of “fairness” with the IOC but Carini has expressed her regret over the row and for failing to shake Khelif’s hand at the end of the bout.

“All this controversy makes me sad,” Carini told the Italian newspaper Gazzetta dello Sport. “I’m sorry for my opponent, too. If the IOC said she can fight, I respect that decision … I have nothing against Khelif and if I meet her again, I will kiss her.”

On Saturday, Bach condemned as “hate speech” the criticism directed by some at two women boxers. “We will not take part in a politically motivated … cultural war”, he said.

He said: “We have two boxers who are born as women, who have been raised as women, who have a passport as a woman and have competed for many years as women. Some want to own a definition of who is a woman.”

The IBA, led by Umar Kremlev, a Russian national and funded by the sanctioned company Gazprom, has said it will pay the winner’s prize of $100,000 to Carini.

Bach responded: “What we have seen from the Russian side and in particular from international federation from which we had to withdraw the recognition, that they have undertaken way before these Games a defamation campaign against France, against the Games, against the IOC. They have made a number of comments in this respect which I don’t want to repeat.”