The leaders of Germany, France and the UK have rejected charges that they are trying to grab power in the EU.
The three countries have tried to reassure other EU members
Gerhard Schroeder, Jacques Chirac and Tony Blair were speaking after talks in Berlin on the future of the European Union and other major issues.
The meeting prompted concerns from some European leaders that the three were trying to dominate an expanded EU.
But Mr Schroeder denied at the end of the meeting that the three were trying to "dominate anyone, let alone Europe".
Mr Blair said it was valuable for the three countries to hold a summit in the wake of what he called "a very difficult period".
France and Germany were among the most vocal critics of the US-led war on Iraq - while London backed Washington equally strongly.
The UK prime minister said everyone would benefit from close co-ordination among the three big countries - which, he said, represented "almost half the population and over half the wealth generated by Europe".
"If we can come to agreement that is a good thing for our three countries, but also for Europe," he said.
France's Mr Chirac rejected the idea that close Franco-German co-operation should be expanded to include Britain, saying Paris and Berlin had a special relationship.
Italy's Europe Minister, Rocco Buttiglione, had warned before the meeting that the EU does not need the triumvirate to run its affairs.
"Nobody in Europe is ready to be a second-class citizen. Europe is made up of 25 countries, not of three," he told the BBC.
Talks among the three leaders focused on economic reform, they said in a closing statement.
They have called for a special EU official with a mission to press for such reforms.
Mr Schroeder said the EU had to become more competitive and streamlined.
British Foreign Secretary Jack Straw said he had spoken to his counterparts in Italy, Spain and Poland over the past two days to reassure them about the purpose of the talks in Berlin.
The leaders of Denmark, Luxembourg and Netherlands have said they were not concerned.
Luxembourg Prime Minister Jean-Claude Juncker told a German radio station that it would be a "useful meeting".
He said it was generally a good idea to co-ordinate positions ahead of EU summits to make actual negotiations easier.
Danish Prime Minister Anders Fogh Rasmussen also said it was "natural for the big countries to get together".
The BBC's European affairs correspondent William Horsley says Mr Chirac and Mr Schroeder now accept that their claim to be the joint "motor" driving Europe's future needs to be adapted as the EU expands to 25 states.
The leaders and their foreign ministers are to discuss wider international affairs over dinner.
Officials say the main focus of the meeting is how to make EU economies more competitive - pushing forward the agenda adopted at the Lisbon summit in 2000.
"Per capita productivity in the EU is still about 20% lower than in the United States," said a British diplomat.
"This is about addressing that."