It comes after the centre was closed this past week by the ICCI's newly appointed board of directors.
It follows a fractious meeting for parents of children attending the religious school last weekend.
The ICCI said that the meeting on Saturday 19 April had been disrupted, and that this had led to security concerns, which made remaining open impossible.
A mosque, religious and national school are located at the site in Clonskeagh.
The Quranic school has not been operating on the site since earlier this month but has re-registered independently of the centre offering classes via zoom.
Today, a lengthy statement from the Nurul Huda Quranic school, stated that all financial information requested by the centre's administration had been provided with full transparency and that this had always been the case.
However, it said that the personal data of parents and students were withheld in compliance with Irish data protection laws.
The statement said that school fees submitted by cash or bank transfer were transferred officially and appropriately to the executive management, and noted that an external audit was conducted annually and had never raised concerns.
The ICCI had stated earlier this week that the board was conducting a comprehensive audit "to address and remedy the legal, financial, and governance issues it has inherited".
The Quranic school said that the current centre management had "sealed our offices and changed the locks without warning on Friday, 11 April" and later "seized control of the school's email accounts (both administrative and teaching staff accounts) in the early hours of Sunday13 April".
It continued that management "bear full responsibility for any data loss or data breaches that may result".
The school's statement said that a meeting will soon be announced via the school’s official channels to present the full facts and respond to any questions.
Meanwhile, the ICCI has confirmed that national school located on the site will operate as normal this week.
Manager of Media Affairs Ali Selim said "the school will reopen today".