The European Union (EU) would not set a deadline to solve the crisis resulting from Ireland's rejection of the Lisbon Treaty, the EU presidency said early Friday.

"It is very sure that we will not set any deadlines, not for Ireland, not for anybody else," Slovenian Prime Minister Janez Jansa, whose country holds the EU rotating presidency, told reporters early Friday following the first day of an EU summit.

The two-day summit, which kicked off Thursday evening, was dominated by the Irish "No" to the Lisbon Treaty in a national referendum last week, which plunged the EU into a political impasse.

As EU leaders were eager to find a rapid solution, they could only agree there was no quick fix at the present stage and more time was needed.

It is very likely that the next EU summit in October "will deal with the question of how to fix the situation after the negative votes of the referendum in Ireland," Jansa said.

Jansa said Irish Prime Minister Brian Cowen explained at the summit the reasons behind his country's rejection of the Lisbon Treaty, but it would take some time to analyze.

Cowen Thursday sought more time from his EU colleagues for his country to find a solution.

"It is necessary for Ireland to have time now to analyze last week's vote and explore options," Cowen told reporters after a pre-summit meeting with the European Commission President Jose Manuel Barroso earlier Thursday.

"In doing so we will be consulting widely at home and abroad. It is far too early yet for anyone to put forward proposals," he said.

Siding with Cowen, Barroso assured that Ireland would be given time to decide how to react and to come forward with proposals on the next steps.

"We both agreed that the next meeting of the European Council in October will be an appropriate occasion for further discussion on this matter," Barroso said, referring to the EU summit in its official name.

Jansa said EU leaders drafted a couple of proposals, without disclosing details but saying those would be under further discussion later today.