The next steps: Mr Valéry Giscard d'Estaing will present the draft constitution approved yesterday to EU leaders in the Greek city of Thessaloniki next week.
But a number of governments have indicated that they will seek changes to the text during an inter-governmental conference (IGC) that will begin in October.
The German Chancellor, Mr Gerhard Schröder, welcomed the draft yesterday but said he would press for the abolition of the national veto on foreign policy issues.
Spain said it would resist a plan to replace the complicated mechanism for calculating a qualified majority agreed at Nice with a simple majority of member-states representing at least 60 per cent of the EU's population.
The convention will meet again next month to finalise part of the constitution that lays down how its provisions are implemented in individual policy areas.
A number of MEPs and national parliamentarians have indicated that they will use the session to demand the extension of qualified majority voting to more policy areas. They also want to introduce a mechanism to allow EU leaders to decide by qualified majority to abolish the requirement for unanimity on some issues.
The IGC, which will begin under the Italian presidency and must end before June 2004, is legally necessary before a new treaty can be agreed. Mr Giscard said yesterday that he would urge EU leaders next week to avoid any substantial reopening of the constitution's key elements.
"I will make just one recommendation to the Council: the closer you stick to our text, which has been discussed and reflected upon at great length, then the lighter will be your task," he said.
The Government's representative at the convention, Mr Dick Roche, said there were a number of issues the IGC will almost certainly have to address. Even if the IGC confined itself primarily to technical redrafting, it could continue into 2004.
"The IGC still has a lot of technical work to do. I still think the IGC will roll over into the Irish presidency, but not for any negative reason," he said.
In a statement yesterday the Commission said it would seek changes at the IGC to a number of the draft constitution's provisions, including the rules governing the composition of the Commission.
"The composition of the Commission could well hamper the operation of the institution, with one commissioner of each nationality and with a difference in status as only 15 commissioners have the right to vote.
"Second, the creation of a more permanent president of the European Council may well upset the institutional balance and cause some duplication with the role of the Commission," the statement said.
The Commission President, Mr Romano Prodi, who has been an outspoken critic of Mr Giscard's handling of the convention, complained yesterday about the absence of any reference to God in the constitution.
"To ignore 1,500 years of civilisation is to create a vacuum in our consciousness, in our identity as Europeans," he said.
The constitutional treaty is likely to be signed next May, when 10 new member-states are due to join the EU. After that, it must be ratified in all 25 member-states.