The President, Mrs McAleese, has praised the EU's draft constitutional treaty but singled out the lack of a reference to God as one that remained to be resolved.
Addressing the European Parliament in Strasbourg, Mrs McAleese said Ireland supported the Italian presidency in its aim to agree a final text for the treaty next month.
"The new treaty will inject a fresh excitement into the Union, transforming its unfortunate bureaucratic image, re-energising its relationship with Europe's citizens, making them feel like insiders and not spectators," she said.
Mrs McAleese said the Convention on the Future of Europe had taken "a huge step forward" in preparing the draft text.
"Naturally, however, a number of questions remain to be fully debated and finally resolved, including the issue of a reference to God in the preamble to the new treaty. The Irish Government has indicated that it would welcome such an inclusion if consensus can be reached on suitable language," she said.
The President's decision to single out the issue of a reference to God caused some surprise in view of the fact that a number of important issues remain to be resolved in the treaty negotiations.
Some observers noted that Mrs McAleese was speaking minutes before the European Parliament was due to vote on a proposal to allow EU funds to be used for embryonic stem cell research which has been opposed by Christian groups.
"It is difficult not to see a linkage," said one senior European Parliament official.
Introducing Mrs McAleese, the President of the European Parliament, Mr Pat Cox, described her as the most popular political figure in Ireland. He said that she had demonstrated during her time as President the benefits of building bridges.
"For me as an Irish European, it's an enormous pleasure to invite you to address this house," Mr Cox said.
Mrs McAleese spoke extensively about the forthcoming Irish presidency of the EU, which she described as the State's most challenging presidency to date.
She said it would be dominated by the accession of ten new member-states to the EU in May, an event she described as lifting the gauntlet thrown down by history.
In an impassioned plea to the EU to look beyond its borders, Mrs McAleese suggested that fighting poverty in the developing world could be the next great challenge facing Europe after enlargement.
"The human misery caused by endemic poverty should shame us but the instability engendered by it threatens all of us.
"Poverty reduction rather than simply poverty management, is fundamental to Europe's future security strategy and we are in an ideal position to champion an end to poverty, disease, corruption, the oppression, the wasteful conflicts and post-colonial malaise which are denying so many human beings the right to a decent life.
"Perhaps this is the new gauntlet that should be thrown down to the 25 member-states of the enlarged Union," she said.