* State-owned bank narrows price range to 4.20-4.60 euros
* Order books on 25 percent sale to close on Thursday
* Proceeds could hit 3.5 bln euros on over-allotment option (Adds details)
By Padraic Halpin
DUBLIN, June 20 (Reuters) - Ireland is set to net at least 3 billion euros ($3.34 billion) from its initial public offering of Allied Irish Banks (AIB) after the bookrunners said order books were covered in the upper half of a narrowed price range.
Dublin launched its long-awaited stock market listing of AIB in May and last week set a price range of between 3.90 euros and 4.90 euros, planning to raise 2.6 billion to 3.3 billion euros from the sale of a 25 percent stake.
Pricing was revised to 4.20 euros to 4.60 euros on Tuesday after books were subscribed multiple times within the initial range. The government will receive 3 billion to 3.1 billion euros if the stock prices in the upper half of the new range.
As the deal also includes a greenshoe or over-allotment option, the size of the IPO could rise to 28.75 percent if demand proves higher than expected following AIB's debut and boost the state's coffers by around another 450 million euros.
The government will use the funds to cut some 1.5 percent from a national debt that at 200 billion euros is still among the highest in the euro zone by most measures.
The float will also be one of Europe's largest bank listings since the 2008 financial crisis and is the biggest test yet of investor demand for a banking sector that required the euro zone's most expensive state rescue less than a decade ago.
One of Ireland's two dominant lenders, AIB needed a 21 billion euro taxpayer bailout to survive a spectacular property crash, the biggest bill for any Irish bank still trading.
But like Ireland's economy, which is growing faster than any other in Europe, the bank has recovered strongly, posting a profit for each of the last three years and becoming the first domestically owned lender to restart dividend since the crash.
Order books will close on Thursday with trading set to commence on Friday, the bookrunners said.
Bank of America Merrill Lynch, Davy Stockbrokers and Deutsche Bank are acting as global coordinators for the sale. Citigroup, Goldman Sachs GS.N, Goodbody Stockbrokers, JPMorgan and UBS are the bookrunners. ($1 = 0.8989 euros) (Reporting by Padraic Halpin. Editing by Jane Merriman and Susan Thomas)