The Taoiseach has said that when he was quoted as saying earlier there would be no bank debt deal for Ireland before the end of the year he was referring to the possible use of the ESM in recapitalising banks.
He said he had made it clear in his response to a question, that the issue of the Anglo Irish Bank's promissory note was separate.
However, the Taoiseach would not be drawn on whether or not this meant a deal on Anglo Promissory notes was still possible before the end of the year.
Arriving at the late night session of summit negotiations in Brussels the Taoiseach said the promissory notes issue was separate and being dealt with between the Minister for Finance, Irish officials and the ECB.
The question of the ESM alleviating Irish bank debt via the other pillar banks was contingent on separate negotiations at eurozone ministerial level which would be taking place next year.
Seven year EU budget
Mr Kenny said that next year's Irish presidency would not "have much authority" in the absence of an agreed budget for the period running 2014-2020.
He added, that it would be difficult for a country, which is coming out of a bailout programme and was facing "considerable burdens", to run an effective presidency if a budget deal was not reached.
Mr Kenny said that as part of the negotiations, which are expected to run throughout the night, he would strongly support EU farm supports under the Common Agriculture Policy.
"It is my intention to argue and negotiate and defend strongly the potential of the CAP and for the potential of cohesion funds with particular reference to employment," he told reporters.
He also said he would argue for the continued EU funding of the peace process in Northern Ireland through the next budget round.
The Taoiseach said tonight's negotiations, which have run two hours late, were starting from a very pessimistic base.
"This is important in the sense of sending out a message about Europe, about European leaders that they actually can come to an agreement for the European uionn, for the eurozone.
"It's important from a global sense," he said.
Taoiseach discussions with French and German leaders
Earlier, Enda Kenny said following his discussions with German Chancellor Angela Merkel and French President Francois Hollande, it had been concluded that Ireland was "a special case".
That will be taken into account during 2013 when finance ministers discuss the creation of a new EU banking union and a banking supervision mechanism, he said.
"We hope that during the course of 2013 our Minister for Finance will progress in that understanding and that decision, and [that] it will be recognised in those discussions," he said.
Mr Kenny said the bank debt issue comprised the recapitalisation of Irish banks, which had already taken place, and the Anglo promissory notes.
He said he hoped both elements required that the level of debt, which he described as a crushing burden, had to be "re-engineered".
The Taoiseach added that Ireland had received "a great deal of support" from the IMF, the ECB, the European Commission and political leaders.
"I hope that being serious ourselves, and proving that we're serious as we manage to move towards an exit of this bailout, that assistance will give us extra help."
Mr Kenny was speaking at the Konrad Adenauer foundation, a German think tank, ahead of the summit of EU leaders in Brussels.
Up to 20 farmers staged a sit-in at Dublin's European Commission office.
The farmers were highlighting their concerns over EU budgetary discussions.
The group, all members of the Irish Farmers' Association took part in a protest earlier in the building.
They have moved into the foyer where they are now staging their occupation.
A number of them have sleeping bags and say they intend staying there until the talks in Brussels are concluded.