Wu's position has been challenged by the AIBA's executive committee, who claim the Taiwanese had led the sport to the brink of bankruptcy.
In a letter to Bach dated September 29, the executive committee (EC) said Wu "has kept hidden... the fact that auditors KPMG are unhappy with AIBA accounts and will not approve them".
"We therefore asked President Wu for a full and open accounting of AIBA finances, which we believe are on the brink of technical bankruptcy or insolvency. President Wu has refused to reply to us," the committee said in the letter.
In reply to the letter sent by the committee to the IOC, Wu posted his own on Monday to "express apology for the inappropriate behaviour by certain AIBA EC members", whose "actions were designed for personal purpose at the cost of boxing's reputation and development".
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"The EC members who are against me understand that AIBA finance is healthy but still make false allegations. Their agenda is self-explanatory," said Wu, who has headed AIBA since 2006.
The International Olympic Committee (IOC) said it had no comment on the letter.
"As a matter of policy the IOC does not respond to open letters," an IOC spokesperson told AFP.
"It has taken note of the court decision against the IMC (interim executive committee) in this internal AIBA dispute.