Irish Prime Minister Bertie Ahern stressed on Sunday that leaders of the 28 current and future EU members agreed to include in the preamble that they "drew their inspiration from the religious inheritance of Europe".
Ahern was responding to a communique by the Vatican saying it regretted that the EU's Christian roots had not been mentioned.
"The vast majority of those religions are based on a belief in God," Ahern said in a statement.
Ireland holds the revolving six-month presidency of the EU and Ahern chaired Friday's meeting that gave the go-ahead for the historic constitution.
"I was particularly pleased that in concluding agreement on the new Constitution, the Irish presidency managed to maintain Article I-51 intact.
"This Article confirms that the Union will respect the status of Churches and that it will maintain an open dialogue with them.
"Senior leaders of many churches have stressed the importance to them of the inclusion of this provision in the Constitution," Ahern said.
Turkey, a Muslim country that wants to join the EU, welcomed the omission of any reference to Christianity.
"It is a constitution that we approve of," Turkish Foreign Minister Abdullah Gul told Anatolia news agency in Brussels on Saturday after EU leaders adopted the text.
"There is no reference (to Christianity). It is a good constitution and it meets Turkey's expectations," he added.
The Vatican and Roman Catholic EU member states -- such as Poland and Spain -- had pressed for the constitution's preamble to refer to Europe's Christian heritage, but without success.
The constitution sets out how the current 25 EU states and any future members divide power between the union's central institutions and individual member countries.
It must now face the hurdle of referendums in several member states before ratification.