EU leaders have agreed to extend the November 2006 deadline to ratify the struggling constitution, but the budget is still overshadowing their summit.
Jean-Claude Juncker (left) is pessimistic about a budget deal
A "period of reflection" would occur after French and Dutch voters rejected the treaty, EU President Jean-Claude Juncker said after talks in Brussels.
However, the UK's budget rebate remains a key area of contention.
London wants any changes linked to a reduction in Europe's farm subsidies, but France refuses to discuss this.
German Chancellor Gerhard Schroeder has urged fellow European leaders to make concessions, saying a deal on the budget will only be possible "if everyone moves".
Correspondents say there is little sign of movement so far.
Friday's talks therefore look set to be deadlocked over the EU's budget for the 2007-2013 period.
UK Foreign Secretary Jack Straw has repeated his threat to veto any attempt to undermine Britain's rebate.
'Answers to questions'
Mr Juncker, Prime Minister of Luxembourg, which holds the EU's rotating presidency, told a news conference the deadline for ratification of the constitution would be extended beyond the current deadline of November 2006.
However, he said there would be no re-negotiation of the constitution, which needs to be ratified by all 25 member states.
"We believe that the constitutional treaty has the answers to many questions that Europeans are asking, so we believe the ratification process must continue," he said.
His comments came as Denmark, Ireland and the Czech Republic said they were postponing planned referendums on the constitution.
European Commission President Jose Manuel Barroso said it was important to consider why French and Dutch voters had rejected the constitution, but it was too early to abandon the treaty.
"We don't want to give up the constitution, nor do we want to carry on with business as usual and pretend nothing has happened," he said.
"We have decided to undertake a stock-taking exercise and have a wide-ranging debate amongst all Europeans. We can't, at the moment, forecast the results of that debate."
French President Jacques Chirac has suggested holding an emergency summit to discuss the EU's future.
"In this new situation, can the union continue to expand without us having the institutions capable of making this enlarged union work efficiently?" Mr Chirac said.
But while the deal to push back the deadline for ratification resolves that issue in the short term, the budget remains deeply contentious.
Prime Minister Tony Blair says any reduction to the UK's 4.4bn euro (£3bn) budget rebate must be tied to changes to farm subsidies, of which France is currently the major beneficiary.
But President Chirac has ruled out any concession on these payments, which were pegged until 2013 in a deal accepted by Britain.
Luxembourg has suggested a compromise which would link the rebate issue to farm subsidy reforms, but allow the UK to keep its rebate frozen at current levels for eight more years.
British officials say the proposal is the same one rejected by Mr Blair earlier in the week.
The Netherlands has also strongly rejected the proposal from Luxembourg, saying it does not address its demand for a huge cut in its financial contribution to the EU.
"The proposals do not go far enough... The Netherlands is the largest net contributor and we want that situation to improve," Dutch Prime Minister Jan Peter Balkenende told reporters.
"We must do something about our position of excessive payments."
Mr Juncker, who made the proposal, has said he is pessimistic about brokering a deal.