In a statement, the bank says a further sum of up to €1bn 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.
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, badly hit by the financial crisis, was nationalised in January.
The Government said in May that it planned to inject up to €4bn into the bank, subject to EU approval.
That announcement came as Anglo Irish reported a pre-tax loss of €4.1bn in the six months to March.
The €3bn is coming from Exchequer cash reserves held by the Central Bank and administered by the National Treasury Management Agency.
