Taiwan’s sports administration has threatened the International Boxing Association with legal action over its “continued publication of false information” in relation to the gender eligibility row at the Olympic Games.

At a chaotic press conference on Monday the controversial ­boxing organisation doubled down on claims that the International Olympic ­Committee had put women’s sport at risk by allowing Lin Yu-ting, representing Chinese Taipei (Taiwan), and Imane Khelif, from Algeria, to compete in Paris.

The boxers, who are assured of at least a bronze medal, had been banned by the IBA from taking part in the world championships last year after the boxing regulator said it ­carried out tests that led to the ­conclusion they did not meet its gender eligibility criteria.

The Russian head of the organisation, Umar Kremlev, said in a rambling video conference call from an office seemingly located in Moscow that the athletes had been found to have “men’s level of testosterone”. He also insulted the IOC president, Thomas Bach, and described the Games opening ceremony as “something horrible for all Christians and Muslims around the world”.

The IBA’s medical ­representative at the press conference, Ioannis Filippatos, and the chief executive of the organisation, Chris Roberts, a former head of Scottish boxing, said that the athletes had chromosome tests rather than one for ­testosterone.

“The results of the chromosome tests demonstrated both boxers were ­ineligible,” Roberts said. He said he could not comment further after receiving letters from the ­Taiwanese and Algerian authorities that morning warning him not to disclose personal information relating to the boxers.

On Tuesday, the Taiwanese sports administration issued a statement making public its discontent with the IBA’s continued commentary on the case that first made headlines after Italy’s Angela Carini abandoned her bout against Khelif after 46 seconds of the fight, claiming she had never been hit harder.

A spokesman said: “The sports administration seriously protests the International Boxing Association’s continued publication of false information, obscuring the facts, and attempting to interfere with the normal conduct of the event regardless of the rights and interests of athletes.

“The Chinese Taipei Olympic Committee has also appointed a lawyer to issue a warning letter to the IBA. It reserves the right to take recourse and will file a lawsuit if necessary.”

The IBA was stripped of its status as a regulator last year over its ­failure to implement reforms on ­governance and finance and the IOC has described the organisation’s alleged tests as lacking credibility. It has said that both boxers are eligible to compete in Paris as they were registered as women at birth and have passports in which they are categorised as female.

The IOC spokesman Mark Adams said the IBA’s press conference in the Salon des Mirroirs function room in central Paris had highlighted the body’s lack of capacity to carry out its role. “I am not going to comment on the chaotic scenes yesterday,’” he said. “It clearly demonstrates that the sport needs a new federation to run boxing.

“If you ever needed any evidence at all that the IBA is unfit to run ­boxing just look at the key members of the IBA who took part in that travesty.”

Adams said that the IOC wanted to see boxing at the 2028 Games but that the sport would need to come together to create a new ­governing body. He said: “We would love to see boxing, we want to see boxing on the programme in LA. Now it is up to the boxing community to organise themselves for the sport and for the athletes.”