Shares in the majority state-owned lender opened 8 percent higher on its return to the main Irish stock exchange on Tuesday after the government sold a quarter of the bank it nationalised almost a decade ago in a 3 billion euro ($3.4 billion) listing.

Ireland's finance minister said following the sale that he could review a pledge to sell a maximum of 25 percent in any of its bank shareholdings by the end of 2018 after AIB hit that limit.

"The opportunity is now stronger. It's like all these things, never miss an opportunity if it's there, at the moment the one thing the government do know is there is demand," AIB CEO Bernard Byrne told Reuters in a telephone interview.

"Ultimately it's their decision but the one thing that has become more obvious is there is lots of demand right now and the Irish story works right now. Those things don't always exists so if you wait for the perfect time, the market may not be there. The market is there right now."

Byrne said investors liked the bank's business model, Ireland's fast growing economy and the fact that AIB would have excess capital available over the next two or three years.

Shares in the third largest European bank IPO since the financial crisis were over four times oversubscribed when they were sold last week. They were trading at 4.73 euros by 0815 GMT, 7.5 percent above the listing price of 4.40 euros.

The size of the IPO is set to rise to 28.75 percent after the government included a greenshoe, or over-allotment, option. The limit on share sales allowed for such an option to nudge it slightly above 25 percent.

The IPO was dominated by institutions happy to take a long-term view of the bank which Byrne said meant the shareholder base was broadly dispersed with very few of sufficient scale that they would have to declare the size of their shareholding.

"A lot of large funds have a good position, not a concentrated position. They have further to go," he said.

He said shareholders had to form their own view on how much capital could be returned to them but added that the bank, which is generating capital each year, plans to return its core tier one capital ratio to 13 percent from the current level of 16 percent once it normalises its stock of non-performing loans.

The Irish government plans to use the proceeds 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.

(Reporting by Padraic Halpin; Editing by Mark Potter/Keith Weir)

By Padraic Halpin