By Jonathan Marcus BBC Diplomatic Correspondent in Brussels

"You might call this a listening tour," said President Bush in answer to one question here at the Nato headquarters in Brussels, and that is not a bad way of characterising this, the president's first foray abroad of his second term.

Mr Bush is in favour of giving Nato a more political dimension

In private, many Nato and European Union leaders remain sceptical about the trajectory of Mr Bush's foreign policy over the next four years.

But the fact that he made the effort to come here is appreciated and the tone that he struck was conciliatory. On a variety of issues he said things that Europeans wanted to hear.

The priority he has given to the Middle East peace process, his willingness to explore the Europeans' diplomatic efforts to resolve the row over Iran's nuclear policy, and his support for European unity - all drew strong applause.

As far as the future of the transatlantic alliance is concerned, Mr Bush has clearly been listening.

Nato reform

A few weeks ago, the German Chancellor Gerhard Schroeder went as far as to suggest that some new forum was needed to discuss contentious issues.

Mr Schroeder's comments reflected a growing sense that for all the talk of change and reform, Nato really does need to look again at the way it goes about its business.

Mr Bush gave his backing to Nato Secretary General Jaap de Hoop Scheffer's plans to give Nato a more political dimension.

The US is trying to improve battered relations with EU allies

This may not go down well with some European leaders who see the EU taking on more of a diplomatic and security role.

But in the future it looks as though such debates will take place within a network of institutions, often with overlapping responsibilities.

The Cold War is now long over and no single institution can expect to monopolise all of the foreign policy debate.

Inevitably, this summit has been strong on symbolism and fairly light on substance.

Managing disagreements

In practical terms, Nato leaders agreed to bring the alliance's training mission in Iraq up to full strength - though some governments like those of France and Germany will continue to make their contribution outside the country.

But there are inevitably going to be bumpy times ahead. When asked about the likely decision of the EU to lift its arms embargo on China, the president was diplomatic.

He restated US concerns about its impact on the balance of power between China and Taiwan. He expressed his willingness to consider the safeguards on arms exports promised by the Europeans.

President Bush dubbed his visit a "listening tour"

But he said that they would have to convince the US Congress of their case. It will be Congress, he noted, that will make the decision on how to react.

So, a fresh start in transatlantic relations? Perhaps. Certainly there will be a renewed effort to turn Nato into a real forum for the crafting of policy on a broader range of issues.

But with the Soviet threat gone there can never be the unanimity within the alliance that there once was. A growing Nato makes things even more complex.

The real issue is not one of ensuring agreement between the US and its European allies. The point is to make sure that in future, disagreements are managed in a proper way and contained.