AIB has offered to buy back subordinated debt from bond holders at a significant discount.
The bank is seeking discounts of up to 90 per cent across a range of notes and bonds.
Bondholders who fail to take up the offer face further steep discounts, paid 1 cent for every €1,000 of debt held, AIB said.
The Government has pledged not to impose losses on senior bondholders, but has backed "appropriate burden-sharing" with the lender's remaining junior bondholders.
Minister for Finance Michael Noonan said the liability management exercise undertaken by AIB was the "final market based step" to ensure this burden sharing.
"The offer prices and the terms of this exercise are fair and balanced relative to the capital requirements of the bank and the level of financial support (in the form of equity, liquidity and guarantees) which the Irish State has so far provided to AIB," he said in a statement.
"It is clear that without such significant financial support, AIB would have become insolvent and subordinated bondholders' entire investment would have been irrecoverable. The proposed LME offers those investors the final opportunity of a market based exit at a return which is reasonable and fair considering the level of Government support to date."
Mr Noonan said if the scheme failed to bring the required gain in core tier 1 capital, the Government would take the necessary steps to achieve at least that level of contribution, with "severe measures" promised in respect of subordinated liabilities if further action was needed.
The subordinated liabilities order made by the High Court under the Credit Institutions Stabilisation Act regarding AIB is currently the subject of a court challenge, with two investors with holdings in three of the 18 affected securities taking action.
Mr Noonan said he considered the challenges, which will come before the court on June 2nd, to be "entirely unfounded".
"The challenges will in no way deter the Government from achieving appropriate burden-sharing of levels broadly consistent with those provided for in this LME with the subordinated bondholders of AIB and of Bank of Ireland, Irish Life & Permanent and EBS," he said.
