Foreign Secretary David Miliband has admitted people's sense of commitment and passion for the European Union is "diminishing".
Following the rejection of the controversial Lisbon Treaty by the Irish people, there was an opportunity to "reflect on the gap between support for the EU and its increasing relevance in the modern world", he said.
But in terms of the institutional debate, "function and purpose" had to be put before EU institutions, he added.
Mr Miliband repeated the British Government's position that there would be no question of "bulldozing or bullying" the Irish, adding there was an opportunity to "clarify and define the role of the EU" in the world.
His remarks will add to the debate among European capitals about how to move forward following the referendum "No" vote in June.
The UK is among 22 of the 27 members to have ratified the Lisbon Treaty, which replaced the failed constitution.
The treaty, which creates the post of a permanent president of the European Council and a single EU representative for foreign affairs, is due to come into effect next year.
But several obstacles remain in the way of its adoption, including the vote in Ireland and court cases in Germany and the Czech Republic.
Speaking at an event at the Mansion House in Dublin, Mr Miliband said: "The situation (over Lisbon) creates an opportunity - an opportunity to clarify and define the role of the EU in the modern world.
"There is a diminishing sense of commitment to and passion for the EU. The situation over Lisbon gives us an opportunity to reflect on the gap between support for the EU and its increasing relevance in the modern world."
