Anglo Irish Bank says the Government has now provided it with €3 billion in capital, following EU approval last week.
In a statement, the bank said a further sum of up to €1 billion was the subject of further discussions between the bank and the Department of Finance on the terms of a debt repurchase programme with Anglo Irish Bank.
AIB and Bank of Ireland have both bought back some of their debt at a discount in recent months, helping their underlying financial strength.
Anglo Irish Bank, badly hit by the financial crisis, was nationalised in January.
The Government said in May that it planned to inject up to €4 billion into the bank, subject to EU approval. That announcement came as Anglo Irish Bank reported a pre-tax loss of €4.1 billion in the six months to March.
The €3 billion is coming from Exchequer cash reserves held by the Central Bank and administered by the National Treasury Management Agency.
