LONDON — The Irish government on Monday announced a price range for Allied Irish Banks that could value the bank as high as $14.9 billion when it goes public this month — seven years after it was nationalized.

The initial public offering is an important milestone in the recovery of the Irish banking system, which nearly bankrupted the country after the financial crisis of 2008.

“The time is right to move to the next stage in A.I.B.’s I.P.O. process as market conditions remain favorable, and I am encouraged by the strong level of interest shown by investors in the offering to date,” Michael Noonan, the Irish finance minister, said in a statement on Monday.

The Irish government injected 21 billion euros, or $23.5 billion at current exchange rates, into Allied Irish Banks, one of Ireland’s largest lenders, in 2009 and 2010 as it suffered under the weight of property loans that went bad amid the financial crisis. The government now owns about 99 percent of its shares.

After rescuing its banks, Ireland was forced to seek its own bailout, receiving €67.5 billion from the European Union and the International Monetary Fund. Ireland emerged from the international bailout program in 2013.

On Monday, the Irish government said it expected to price the offering of Allied Irish Banks from €3.90 to €4.90 a share. That would imply a market capitalization of €13.3 billion at the upper end of the range.

The offering,…