* Uncertainty over deal to let banks tap euro rescue fund
* PM Kenny says imperative that summit decisions honoured
* EU's Barroso says clear agreement made to use ESM fund
By John O'Donnell
BRUSSELS, Oct 3 (Reuters) - Ireland urged euro zone leaders on Wednesday to stick to a deal allowing the bloc's rescue fund to assist its ailing banks, in a move to head off threats that the agreement could be unwound.
Prime Minister Enda Kenny's message, which won tacit endorsement from one of the EU's top officials, underscored Dublin's growing concern that the agreement, sealed at a summit in June, may be amended.
Using the ESM rescue fund to recapitalise lenders directly would help Ireland draw a line under its banking problems, easing its full return to debt markets and ensuring it does not need further financial aid.
Euro zone leaders said in June they would allow this as soon as a new system of supervision was in place, in an effort to break the negative link between troubled banks and the governments that were often forced to bail them out.
But last month, this pledge looked at risk when Germany, the Netherlands and Finland laid out terms under which they would allow the ESM to grant such assistance.
They made a distinction between future banking problems and "legacy" difficulties, which some analysts interpreted as saying that existing bank problems in Spain and Ireland would remain the responsibility of those countries.
"It is particularly important that there be a real emphasis on bringing to a conclusion the clear, unequivocal decision made (at the June summit)... in regard to breaking the link between sovereign debt and bank debt," Kenny told journalists on a visit to Brussels.
Ireland, which takes over the six-month presidency of the European Union in January, was forced to seek a bailout after it had to prop up its shattered banking sector.
"It is imperative that citizens ... can have demonstrated to them that (such) decisions ... are followed through," said Kenny, who met European Commission President Jose Manuel Barroso and Herman Van Rompuy, who chairs European summits.
Barroso appeared to side with Kenny, telling journalists that agreement had been "clearly" made to allow the ESM help banks directly.
Jean-Claude Juncker, who chairs meetings of euro zone finance ministers, told EU ambassadors at a meeting this week that direct recapitalisation of lenders should not be limited to a bank's future problems, said one EU official.
Giving direct aid to banks instead of via their home country stops those governments racking up debts to help their lenders.
European policymakers are keen to sell Ireland as a success story and proof that their management of the crisis has worked - at least for Dublin, which has stuck by a programme of tough fiscal reform.
In July, Ireland sold new long-term government bonds for the first time since 2010, offering a rare glimmer of hope in the European debt crisis.
Ireland's cost of borrowing has tumbled since euro zone leaders committed to examine bank recapitalisation and to lightening Ireland's debt burden in late June. The yield on its benchmark 10-year bond has fallen to around 5.1 percent from 7.5 percent earlier this year.
This means that Ireland can now borrow more cheaply than Spain, which is not on euro zone emergency funding, and pay only marginally more than the euro zone's third-biggest economy, Italy.
While Dublin has been focusing on trying to change the repayment terms associated with recapitalising two failed, state-owned banks, it also hoped to benefit from direct recapitalisation.
Shifting the bank stakes off the government's books would the clear the state of having to foot any future costs, a risk with mortgage arrears continuing to rise.
(Reporting by John O'Donnell; Additional reporting by Luke Baker in Brussels; Editing by John Stonestreet)
Keywords: EU IRELAND/