Leaders also pushed Friday for a new U.N. Security Council resolution to expand the United Nations' role in Iraq ahead of the U.S. handover of sovereignty, but they left the details vague.
The "Big Three" leaders of Germany, Britain and France, meanwhile, revealed they would hold their own get-together on homeland security after the adoption of new EU anti-terrorism measures.
The leaders, who began a two-day summit on Thursday, picked former Dutch government official Gijs de Vries as the bloc's first anti-terror czar to bolster the continent's defense after the March 11 bombings in Madrid, which are suspected to have been carried out by Islamic radicals.
"The tragic events of two weeks ago, it has certainly made people reflect and contemplate," Irish Prime Minister Bertie Ahern said Thursday.
"This has been a difficult few weeks for Europe," he said. "There was pressure on all of us."
Ahern, whose country holds the EU presidency, also said leaders agreed to try for a deal on a constitution by June 17 — six months after the draft was supposed to have been approved.
Talks collapsed last December after Poland and Spain, which would have seen their power reduced, refused to go along. The constitution must be agreed unanimously by all 15 current and 10 soon-to-be EU members.
Ahern will pursue one-on-one negotiations with a view to sorting out the most divisive issues before convening another summit.
"Obviously there is a lot of work to do," he said. "Everyone understands there will have to be compromises."
EU officials acknowledge that another collapse in talks this year would spell disaster for the 465-article draft constitution, which was put together by a 105-member constitutional convention over the past two years.
European Parliament President Pat Cox said the EU "should refuse to contemplate failure" in the talks.
Optimism has surged since the March 14 election defeat of Spanish Prime Minister Jose-Maria Aznar's conservative party by Jose Luis Rodriguez Zapatero, a socialist, who is more eager to find a breakthrough.
As a result, Poland also eased its opposition to the charter.
"The Polish government is open to dialogue," said Polish Prime Minister Leszek Miller. His popularity ebbing, Miller announced later Friday that he would step down as soon as his country joins the EU and a successor is named.
In addition to a voting formula, Ahern said about 20 items remained to be resolved, including the size of the EU's executive commission and the number of European Parliament seats.
"I think we can get a basis for agreement on those," he said.
The constitution is meant to streamline decision making in a bloc of 25 nations and bolster its role on the world stage, with the creation of an EU president and foreign minister. It also boosts defense cooperation.
De Vries will coordinate work done by the EU's foreign affairs and interior departments in an echo of the U.S. Department of Homeland Security, which was created after the Sept. 11, 2001, attacks.
De Vries, a former deputy interior minister, was born in New York and holds joint U.S.-Dutch citizenship. He will start work Monday and report to Javier Solana, who heads the EU's foreign and security department.
"He has the right profile for the position," Solana said. "What is important is coordination. All the internal, domestic aspects of terrorism need to be tied in with the external, international aspects."
The summit also adopted measures creating an EU-wide arrest warrant, cracking down on terrorist finances, creating a database of terrorism suspects and improving border controls.
The Iraq declaration adopted at the end of a two-day summit did not directly link a new U.N. resolution to a willingness to supply peacekeepers for the Iraq mission.
It stated that EU leaders "look forward to the U.N. playing a vital and growing role endorsed by the U.N. Security Council in the run-up to transition and beyond."
Diplomats said discussions had only begun on details and there were still differences on how much bigger the U.N. role should be.
But they noted the "balance had shifted a bit" in the EU since Aznar's defeat.