Europe has displayed an impressive discipline in its response to the terrorist assault against the US. After an outpouring of sympathy came a powerful expression of collective resolve when Nato invoked article 5 stating that an attack on one member was an attack against the alliance.

Now comes the hard part. The intense diplomacy across the Atlantic this week underlines concern in European capitals about how the Bush administration intends to manage the next phase of the crisis. A military response is inevitable. But the timing, the targets - and above all the objectives - in the new war on terrorism remain unclear.

Tony Blair, who follows Jacques Chirac to Washington, will naturally want to influence the administration's deliberations. Britain, France and the rest of the European Union want to know what the international coalition against terrorism is ultimately for. Is it a broad alliance with the narrow objective of punishing the perpetrators, or does President George W. Bush favour a narrow US-led coalition with the broad objective of a war against terrorism around the globe?

Mr Bush's Wyatt Earp rhetoric gives the impression of a trigger-happy president. But his pledge to bring Osama bin Laden, the fugitive Saudi terrorist, to justice "dead or alive" is more geared to an American audience bent on revenge. In practice, the White House seems more circumspect. As Mr Bush told Congressional leaders: there is not much point in dispatching $2m missiles to destroy an empty $10 tent.

Europe's leaders should reinforce the case for proceeding carefully - but not to the point of ruling out any action that could risk civilian casualties. The issue should not be whether the retaliation should be proportionate, but whether it is precise if it comes to commando strikes against Mr bin Laden's camps in Afghanistan.

This will be the first phase of the war on terrorism. The second will be a wider onslaught on the regimes which support terrorism as well as their financial networks. This will have far-reaching repercussions since it could include countries such as Libya, Iran and Iraq. Europe will want to have a say in this second phase; but EU leaders must realise that their influence will depend on their commitment to the first military phase of the war.

The international coalition will come under increasing strain in coming weeks. But if European countries break rank, they cannot expect a fair hearing in Washington. Equally Mr Bush should take note of the efforts which EU governments are taking this week to strengthen counter-terrorism. For this is the arena where ultimately the war can be won.