The IOC said it wrote a letter to IBA President Umar Kremlev (40) and ordered a full review of the embattled IBA's progress on reforms.
It was responding to a letter by Kremlev this week that said the federation was concerned about confidential data relating to its competition officials after they were contacted by the IOC in relation to Paris 2024 boxing qualifiers.
The IOC suspended the IBA in 2019 over governance, finance, refereeing and ethical issues and did not involve it in running the boxing events at the 2021 Tokyo Olympics.
The IOC will also be in charge of the boxing qualifiers for the Paris Olympics.
"The allegations contained in your letter, in particular those relating to the integrity of the process (of contacting judges), are generally refuted," the IOC said in its letter to the IBA.
The IOC said it had ordered an analysis of all reform elements that the IBA has been instructed to undertake in order to be reinstated again.
"The IOC can only accept a sport where there has been a full and fair qualification process," IOC spokesperson Mark Adams told a news conference.
"To make it absolutely clear. The IOC has no problem with the sport of boxing or the boxers but there are problems with the suspended federation."
The IBA had said it its letter that the Olympic body's actions were in breach of a data transfer agreement signed in 2019.
It would "reserve all rights to seek redress before the competent court against IOC to request damages for breach of the agreement, illegitimate use of our intellectual property and breach of the General Data Protection Regulation amongst other breaches in which the IOC has committed."
The IOC in turn warned that such a move would have serious consequences.
"If the IBA pushes ahead with these proposals it will have quite some consequences," Adams said.
The IOC has said repeatedly that boxing risked losing its spot at the 2028 Los Angeles Olympics if the federation did not reform.
Relations between the IOC and the IBA further soured following Russia's invasion of Ukraine last year, with the IBA run by Russian Kremlev and with Russian energy firm Gazprom being its main sponsor.
