DUBLIN (Reuters) -The Irish government on Monday launched the sale of its remaining shares in AIB Group, one of the country's two dominant lenders it effectively nationalised 15 years ago, Finance Minister Paschal Donohoe said.

Ireland pumped 64 billion euros ($74.10 billion) or almost 40% of its then annual economic output, into the country's banks after a huge property crash in the late 2000s stemming from the global financial crisis. Two banks that swallowed up more than half of the capital still failed.

Most of the remaining funds - 21 billion euros - went into AIB and the state's return from the bank stood at 19.2 billion euros last month when its shareholding dropped to 3.3%. AIB is also it talks to buy back stock warrants the government holds in the bank.

The transaction will leave Ireland with a 57% stake in the smaller Permanent TSB to sell to complete its long withdrawal from the sector. It sold the last of its shares in AIB's chief rival Bank of Ireland in 2022.

"This is an important milestone in delivering on the policy of returning the banking sector to private ownership," Donohoe said, announcing the sale of the state's final 2% holding by way of an accelerated bookbuild transaction.

The government has sold small amounts of shares between its bigger transactions, resulting in the now 2% holding.

Books on the transaction are covered, a bookrunner on the deal said shortly after it was announced.

While Dublin is unlikely to fully recoup the cost of bailing out AIB, Donohoe said last month the state was at that point 300 million euros above break-even on its 29.4 billion investment in the three banks, mainly thanks to recovering 6.7 billion euros from the 4.7 billion it pumped into Bank of Ireland.

The government removed a 500,000 euro pay cap from Bank of Ireland after completing a review of the sector's pay restrictions shortly after the bank returned to full private ownership. The cap remained in place for AIB and Permanent TSB.

($1 = 0.8637 euros)

(Reporting by Padraic HalpinEditing by Tomasz Janowski and Alison Williams)