Shutting the National Asset Management Agency (Nama) will be good for the economy, but lenders like Ulster Bank need to make clear whether they are staying or going, according to Bank of Ireland boss Richie Boucher.
The bank's chief executive said he always felt the Nama would make money over its lifetime.
"Nama's exit will be another positive for the economy, whether it happens in 2017 or in 2020," Mr Boucher told reporters yesterday.
He was responding to suggestions the agency could now be closed down ahead of schedule, by selling off loans more quickly than first planned.
Bank of Ireland will be repaid around €4bn (£3.3bn) when that happens.
Bank of Ireland suffered a pretax loss of €569m (£468m) last year but is now profitable, the bank said yesterday.
It has 35 branches in Northern Ireland and employs around 1,200 staff.
Richie Boucher said he would welcome a new banking force in the Republic, saying having just two big banks in AIB and his own lender is too few for the economy.
But in a reference to speculation around Ulster Bank's plans here he warned that banks need to make clear their position so that customers can plan.
"Its not helpful to have this Lannigan's Ball where you don't know whether they are in or out," he said.
Bank of Ireland's loss of €569m (£469m) is compared to its €1.4bn (£1.1bn) loss in 2012. The bank reported a steady improvement in the Irish economy during 2013.
In its full-year results for 2013, the bank says its operating profit, before impairment charges, was just over €1bn, up from €224m (£184m) the year before.
Mortgage arrears and small businesses in trouble remain key priorities, the bank says.
The majority – eight out of 10 – of its "challenged" Irish mortgages with agreed restructuring solutions are meeting repayments.
The level of defaulted loans has fallen by €1.2bn (£0.9bn), or by 6% since June 2013.
The bank has reached a resolution with SME loans in more than 90% of cases.
Mr Boucher said Bank of Ireland is profitable and generating capital this year.
"2013 was a year of further substantial progress for Bank of Ireland," he said.
"Taxpayers' support for and investment in Bank of Ireland has been rewarded and repaid. We are profitable and generating capital in 2014."
Davy Stockbrokers said the results were strong, with the bank's finances showing it was making profits before provisions ahead of expectations and was also generating capital.
The annual report showed the breakdown of impairment charges for loans with residential mortgages costing the bank €573m (£472m) last year.
Property and construction lending cost €583m (£480m).
Mr Boucher said a key priority remains the solution of Irish mortgage arrears and challenges facing small and medium enterprises.
And he said that eight out of 10 debt-hit Irish mortgages which have been restructured are now being repaid as required.
The bank also said about €6bn (£4.9bn) has been returned to the state following the bailout.
"It is right and appropriate that taxpayers have got back their cash investment in Bank of Ireland, with a cash profit achieved and considerable potential upside," Mr Boucher said.
Bank of Ireland has more than 280 branches, 1,400 ATMs, and employs more than 11,255 staff.