The European elections have been characterised by anti-government votes and low turnout in most member states.
While conservative parties keep control of the parliament, Eurosceptic and far-right parties have taken up to 15% of the seats.
Their breakthrough raises questions over the EU constitution, which is due to be finalised at the Brussels summit later this week.
The Minister for Foreign Affairs, Brian Cowen, who has been in Luxembourg presenting ministers with treaty amendments, says he is confident a deal on the EU constitution will be reached.
The President of the European Parliament, Pat Cox, emphasised the large scale of the elections, but said governments should have done more to mobilise voters in the newer states.
