EU foreign ministers have begun a two-day meeting in Naples to try to narrow differences over a draft constitution.
The atmosphere has been soured by rows over budget deficits
The European Commission has said there is a risk of failure unless the 15 member states make compromises.
On Friday, UK Foreign Secretary Jack Straw said the UK would reject the draft constitution if states would lose their veto over foreign policy.
EU president Italy hopes to reach final agreement on the text in two weeks, but analysts say this is highly optimistic.
The EU constitution is designed to bring it closer to citizens, and to streamline decision-making in the future enlarged union of 25 nations.
In addition to Britain's concerns about foreign policy, Spain and Poland are resisting efforts to reduce the number of votes they wield.
Proposal for majority voting on foreign policy
National voting weights in the Council of Ministers
The number of commissioners
Mention of Christian heritage
Small countries are fighting to ensure that each country will still have its own European commissioner with full voting rights.
There is also controversy about whether or not to include a reference to Europe's Judaeo-Christian heritage in the preamble to the constitution.
The BBC's diplomatic correspondent Barnaby Mason says the disputes make the task of the Italian presidency look almost impossible.
Small states' anger
Thousands of police are on the streets of Naples to ensure security during the meeting.
Interior Minister Giuseppe Pisanu told Italian newspapers about the threat of attacks from terrorists who "could mingle with immigrant groups who try to arrive clandestinely in our country".
Anti-globalisation protesters are also due to hold demonstrations outside the conference venue on Saturday.
The meeting started on Friday with the European Commission - the EU's executive body - having lost face this week in failing to get backing for moves to discipline France and Germany over their budget deficits.
Diplomats say this Franco-German victory - achieved with the support of Italy - has soured the atmosphere at Naples, and increased the feeling among small nations that the balance of power in the EU is shifting in favour of the big countries.
Italy has floated a number of amendments to the constitution drafted by a convention under France's former president, Valery Giscard d'Estaing.
The proposed changes include allowing foreign policy decisions to be made by a majority vote - instead of by unanimous vote, as at present.
London said this week that any effort to change the existing system would cross a "red line" - prompting a UK veto.
This and other major disagreements are expected to be left for heads of state to resolve at a summit in Brussels on 12 and 13 December.
Poland and Spain insist on keeping the disproportionately large number of votes they were promised at the Nice summit in 2000.
Small countries such as Finland are resisting efforts to hold the number of voting commissioners at 15 - meaning 10 countries would not have fully-fledged commissioners when the union expands.
Opponents say that a commission of 25 would be too unwieldy to work effectively.
The foreign ministers, whose goal is to pave the way for success at the Brussels summit, will meet for a last time on 9 December.
If the draft constitution is not agreed this year, talks will continue next year under the Irish presidency.
The ratification process is due to start in mid-2004, and the constitution is expected to come into force in 2006 at the earliest.