It is better to have no deal on an EU constitution than to have a bad one, Italy's prime minister has said.
Berlusconi says the constitution must be right
"If [negotiations] can't be concluded by Sunday morning, it would be better to continue [talking] than to make a bad deal," Silvio Berlusconi said.
A battle over the relative power of large and medium-sized countries may wreck efforts to approve a constitution at the Brussels summit this weekend.
The task is critical for the EU, which is set to grow from 15 to 25 members.
Mr Berlusconi, the summit host, warned that the dispute over how many votes countries have might "block the whole agreement".
If leaders fail to agree a deal at this weekend's summit, the problem passes to Ireland, which takes over the European Union presidency from 1 January.
Number of commissioners
National vetoes on foreign, defence and taxation policy
Extent of European Parliament's influence on EU budget
Ireland's Europe minister told reporters he was praying a compromise would be reached this weekend.
Describing a picture of Mr Berlusconi, apparently in prayer, in an Irish newspaper, Dick Roche said: "I can assure you the Irish team are praying even more fervently."
The summit is scheduled to last two days, but it could well turn into a marathon haggling session, observers say.
Although huge disputes loom over the conference, the event began positively.
Leaders have already reached agreement on:
- A multi-billion-euro scheme to encourage investment in the EU's flagging economy
- A defence planning cell independent of Nato
But they still face the most difficult challenge: Ironing out differences between the proposed constitution - the European Union's first ever - and a deal made in Nice three years ago.
The BBC's Tim Franks in Brussels says that in the best tradition of market hagglers, leaders have been warning that they are prepared to walk away rather than buy the constitution on offer.
VOTING RIGHTS OPTIONS
Nice agreement: Favours mid-sized states like Spain and Poland, which get voting powers comparable to a giant like Germany
New constitution: Favours large and small countries by requiring support of a majority of member states representing at least 60% of the EU's population
All 25 leaders must approve the new constitution.
The Nice deal gave Spain and Poland more votes than their population sizes warrant, and both countries are reluctant to give those votes up.
"If we fail, it will be caused by all of us, not just Poland," Foreign Minister Wlodzimierz Cimoszewicz told reporters on Friday.
The French President, Jacques Chirac, has criticised Spain and Poland, saying they were not following democratic rules.
He added that founder members of the EU such as France and Germany would not accept a distortion of their vision of Europe.
Ordinary Europeans, for their part, have told the BBC they have little understanding of what the leaders are talking about.
In Paris, people who spoke to the BBC's World Today programme either said they had "no idea" or hoped it would be a "constitution like the French one with liberty, fraternity and peace in the world".
Poland's Kwasniewski is standing firm over voting rights
The new constitution, drafted over 17 months by a special convention, introduces a "double majority" system of voting.
It means a vote is passed when it has the support of 50% of countries, representing 60% of the EU's population.
Medium-sized countries like Poland and Spain say the system favours big states - like Britain, France and Germany - and the very smallest nations.
UK Prime Minister Tony Blair has said he has "red lines" on other issues, such as countries' right to veto EU decisions.
Mr Blair is expected to insist on retaining the national veto in key policy areas such as taxation, legal systems, social security provisions and budgets.
Another contentious issue raised by Poland is the lack of any mention in the constitution of Europe's Christian heritage and values.
However, the EU leaders began their talks by announcing agreements on defence, security and investment.
The leaders approved plans presented by Britain, France and Germany to create an EU military planning cell independent of Nato early in the new year.
A "quick start" plan to encourage public and private investment in transport and research was also announced.
Worth 62bn euros, it covers projects ranging from Alpine rail tunnels to laser technology research.