The Hungarian Boxing Association has protested to the International Olympic Committee over its decision to allow the Algerian fighter Imane Khelif to compete at Paris 2024, before her quarter-final bout with one of its boxers.

The Hungarian fighter Anna Luca Hamori is due to fight Khelif on Saturday as a gender eligibility storm around women’s boxing at the Paris Olympics continues.

Khelif won her fight against the Italian Angela Carini on Thursday and on Friday Chinese Taipei fighter Lin Yu-ting, the second boxer at the centre of the controversy also won, outpointing Uzbekistan’s Sitora Turdibekova.

Related: Angela Carini abandons Olympic fight after 46 seconds against Imane Khelif

The presence of Lin and Khelif has come under intense scrutiny at these Games. Both fighters competed without incident at Tokyo 2020, but were disqualified from last year’s world championships at a late stage by the International Boxing Association (IBA) for failing to meet gender eligibility criteria.

Lin and Turdibekova touched gloves after their bout, but did not embrace or shake hands, with the defeated boxer leaving the ring quickly and declining to comment on the fight. Lin, the top seed in the women’s 57kg category, will now fight in the quarter-finals against Bulgarian Svetlana Staneva, who beat Ireland’s Michaela Walsh.

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”. On Friday she said she wanted to apologise to her opponent for not shaking hands.

“All this controversy makes me sad,” Carini told Italian newspaper Gazzetta dello Sport. “I’m sorry for my opponent, too. If the IOC said she can fight, I respect that decision.”

Lajos Berko, a member of the Hungarian Boxing Association’s executive board told Hungary’s state news agency MTI that their boxer Hamori will fight Khelif in their bout on Saturday.

But Berko said the Hungarian Boxing Association would protest to the IOC and request it to reconsider the decision to allow a previously banned boxer to fight. The association is also writing to the Hungarian Olympic Committee. It was investigating the possibility of legally challenging Khelif’s presence, he added. “I am very sad that there is a scandal and that we have to talk about a topic that is not compatible with sport,” Berko said. “This is unacceptable and outrageous.” The Hungarian Olympic Committee itself called for talks with the IOC to protect “the right of female competitors to equal opportunities and fair competition”.

Hamori is Hungary’s first women’s boxer at the Olympics. After winning against Australia’s Marissa Williamson Pohlman in the 66kg category, she said she had no qualms about facing Khelif. “I’m not scared,” Hamori said. “I don’t care about the press story and social media.”

But in a social media post Hamori said: “In my humble opinion I don’t think it’s fair that this contestant can compete in the women’s category … but I cannot concern myself with that now. I cannot change it, it’s life.”

The IBA is not running the ­Olympic boxing competition after it was expelled from the Olympic movement for failing to reform judging and refereeing, financial stability and governance issues. The IOC has confirmed it is happy for both fighters to compete under the less strict gender eligibility rules that were in place for the Tokyo Games in 2021.

The IBA president, Umar Kremlev, last year said of the fighters that DNA tests had “proved they had XY chromosomes and were thus excluded”. It is not known what tests they underwent, and the IOC criticised the IBA for changing its gender rules in the middle of the 2023 world championships.

On Thursday night the IOC said: “The two athletes have been competing in international boxing competitions for many years in the women’s category, including the Olympic Games Tokyo 2020, International Boxing Association (IBA) world championships and IBA-sanctioned tournaments. These two athletes were the victims of a sudden and arbitrary decision by the IBA. Towards the end of the IBA world championships in 2023, they were suddenly disqualified without any due process …

“The current aggression against these two athletes is based entirely on this arbitrary decision, which was taken without any proper procedure – especially considering that these athletes had been competing in top-level competition for many years.”

Previous disputes over gender eligibility in sports have centred around athletes with differences in sex development (DSD); it is not known if this applies to the two fighters at the centre of the dispute. Middle-distance runner Caster Semenya, who was legally identified as female at birth but has a condition which means her body naturally produces higher levels of testosterone than women without the condition, won a ruling of discrimination at the European court of human rights, but an appeal is ongoing.

Lisa Nandy, the UK culture secretary, described the Olympic boxing bout between Khelif and Carini as “an incredibly uncomfortable watch”.

Nandy acknowledged concern about “getting the balance right” in boxing and other sports when it comes to female competitors. But she said the “biological facts are far more complicated than is being presented on social media and in some of the speculation”.

She said: “I think as sporting bodies try to get that balance between inclusion, fairness and safety, there is a role for government to make sure that they’ve got the guidance and the framework and the support to make those decisions correctly and it’s something that I’ll be talking to sporting bodies about over the coming weeks and months.”