IBRC Chairman Alan Dukes has criticised Minister for Transport Leo Varadkar for "gratuitously insulting" senior management at the bank.
Mr Dukes was responding via email to comments by the minister on pay levels at the nationalised lender last month.
His email was released under Freedom of Information to RTÉ News by the Department of Transport.
Mr Varadkar was quoted in a Sunday newspaper on 11 November as saying: "IBRC and State controlled banks must respond swiftly to the growing demand for action on pay and pensions".
In his email of 12 November, Mr Dukes takes issue with Mr Varadkar, who also said that the people who contributed to the crisis should shoulder a portion of the burden.
Mr Dukes says, with the exception of IBRC's manager of IT and operations, all of senior management at the bank "have been recruited outside the Irish banking system".
He adds: "Your gratuitously insulting characterisation of these people is akin to blaming the team in the intensive care unit for the heart attack that brought the patient there in the first place."
Mr Dukes also takes issue with the minister describing IBRC as a debt collector.
He says: "A simple 'debt collector' would not have succeeded in 2011 in one of the largest asset disposals ever seen in the US market to the complete satisfaction of the Minister for Finance."
He adds that in April, Minister for Finance Michael Noonan asked if the board would consider a cut in salary.
Mr Dukes says he sent a reply outlining why directors did not consider this "a wise or safe course, in the interests of the State".
He says appointments at IBRC receive the consent of the Finance Minister.
Mr Dukes also questions calls for a merger of IBRC with NAMA, and says the agency does not have the resources to manage all of the bank’s loans.