Prime Minister David Cameron has clashed with French President Nicolas Sarkozy over the UK's involvement in discussions about the eurozone crisis.
Mr Sarkozy believes the final talks on Wednesday should be limited to nations which actually use the euro.
Mr Cameron said all EU leaders should be present to debate issues which could affect them in one way or another.
The clash came on the day when leaders agreed to change the Union's treaty if necessary to help resolve the crisis.
EU president Herman Van Rompuy said after a day of emergency talks in Brussels that members would "explore the possibility of limited change".
Mr Cameron said he had sought assurances to protect the UK's interest if there is change.
All EU leaders are now set to attend the final meeting on Wednesday, which was originally meant to be attended by only the 17 countries that use the euro.
That prompted French leader Mr Sarkozy to speak out. He said he was sick of reading in newspapers about advice Mr Cameron and his Chancellor George Osborne were offering the eurozone.
At one point in the exchanges, Mr Sarkozy was quoted as telling Mr Cameron: "We are sick of you criticising us and telling us what to do."
On Sunday morning the leaders of all the European Union's 27 members held talks about the Greek debt crisis, recapitalising banks, and bolstering the bailout fund.
This was followed in the afternoon by a separate meeting of the 17 nations that use the euro.
Speaking after the meeting, Mr Van Rompuy said that altering the treaty was under discussion. Although no proposed details were given, any change is likely to involve closer fiscal and economic cooperation.
"The aim is deepening our economic convergence and strengthening economic discipline," Mr Van Rompuy said.
He said the words "limited change" meant "not a general overhaul of the institutional architecture".
He added: We also said that we would need the agreement of all the 27 (member states) before we can decide on a treaty change."
Mr Cameron said he had secured safeguards to ensure that Britain's national interest within the EU was protected as the eurozone nations moved towards greater fiscal and economic integration.
He told a news conference: "This must not be at the expense of Britain's national interest. I have secured a commitment today that we must safeguard the interests of countries that want to stay outside the euro, particularly with respect to the integrity of the single market for all 27 countries of the EU."
The prime minister said the EU needed to build on the progress of the work done on Saturday on recapitalising the banks.
"More progress is needed. I think we are beginning to see the elements of a strong package coming together," he said.
Mr Cameron has cancelled visits to Japan and New Zealand this week in order to attend Wednesday's summit.
Speaking alongside German Chancellor Angela Merkel at a joint press conference on Sunday, Mr Sarkozy said "a quite broad agreement was taking shape on the reinforcement" of the bailout fund.
Mrs Merkel said a French idea for the fund to acquire a banking licence was dead, leaving a mix of plans to use the fund to offer insurance to eurozone bond holders, and moves to create a "fund within the fund" that would be topped up by some of the main emerging nations.
On Saturday eurozone finance ministers struck a provisional deal that will see banks raise more than 100bn euros (£87bn) in new capital to shield them against possible losses to indebted countries.
It is conditional on a wider accord, including a write-down of Greek debt.
BBC business editor Robert Peston said the 100bn euros agreed in the deal will be provided to banks by commercial investors, national governments and the EU's bailout fund.
Debt-laden Greece has been bailed out - twice - along with the Irish Republic and Portugal.
The eurozone is working on a third package for Greece, as well as a solution that could help the much bigger economies of Spain and Italy, which are faltering.