British PM Theresa May was not invited to the talks
Taoiseach Enda Kenny says he explained to European Union leaders the difficult position that Ireland is in with regard to the UK decision to leave the EU.
The 27 leaders from the EU have completed a summit without British Prime Minister Theresa May in Bratislava.
Donald Tusk, the president of the European Council, warned leaders in a frank letter earlier this week that the migration crisis would be top of the agenda, as EU citizens felt a "tipping point" was reached during last summer's crisis.
In his open letter following a tour of EU capitals including London, Mr Tusk said the EU had to confront its shortcomings.
He wrote: "It would be a fatal error to assume that the negative result in the UK referendum represents a specifically British issue.
"The Brexit vote is a desperate attempt to answer the questions that millions of Europeans ask themselves daily.
"Questions about the guarantees of security of the citizens and their territory, questions about the protection of their interests, cultural heritage and way of life.
"People in Europe want to know if the political elites are capable of restoring control over events and processes which overwhelm, disorientate and sometimes terrify them. Today many people, not only in the UK, think that being part of the European Union stands in the way of stability and security."
Mr Tusk chaired the meeting, which EU sources said the migration crisis, risks of terrorism and people feeling alienated by globalisation would be the three main topics on the agenda.
Mrs May, who saw Mr Tusk in London last week, will be updated on the discussion when they next speak.
Mr Kenny also says the Apple tax ruling did not arise during the meeting.