The French President, Mr Jacques Chirac, has welcomed the fall of Saddam Hussein but stressed that power should be returned to the Iraqi people as soon as possible.
Mr Chirac, who led European opposition to the war in Iraq, said that it was essential that the United Nations should play a central role after Iraq had been stabilised.
"As soon as possible, after the necessary phase of securing it, Iraq must return to its full sovereignty in a stabilised region with the legitimacy of the United Nations," he said in a statement.
The French Foreign Minister, Mr Dominique de Villepin, also welcomed the coalition's military success and called for the international community to work together to give Iraq a better future.
But Mr Alain Juppe, a former French prime minister and now an aide to Mr Chirac, said that events in Iraq had shown that France was right to oppose the war.
"We were right to say that there were other ways to disarm Iraq. Iraq did not use weapons of mass destruction," he said.
Germany's Chancellor, Mr Gerhard Schröder, said yesterday that the coalition's success did not undermine Germany's case for opposing the war. He said that the people who died in Iraq during the past three weeks did so because of a political decision.
"This was always going to end in a military victory for the allied forces and that was to be wished for. But one must not forget that war always claims many victims and that this one claimed a lot of victims, too. I have no reason to depart from my basic position," he said.
Mr Schöder said that Germany would only participate in the reconstruction of Iraq if it was under UN auspices and he gave a cautious welcome to assurances from Britain and the US that the UN would play a "vital" role in post-war Iraq.
"We will have to see what is meant by a 'vital' role. I think if you want stability in the region and lasting peace, one needs the UN, and my impression is that this is also in the interests of the Americans and British," he said.
Mr Schröder and Mr Chirac will discuss Iraq with the Russian president, Mr Vladimir Putin, in St Petersburg today.
Mr Schröder yesterday played down the meeting's significance and insisted that it was not intended as a provocation against Washington.
"It's quite a normal meeting that was arranged a long time ago and it is directed against no one," he said.
Mr Schröder said it was "macabre" to start talking about which companies should receive contracts for the reconstruction of Iraq before hostilities had ended. However, the European Commission said yesterday that it was examining contracts for post-war Iraq awarded by the US government to ensure that they complied with World Trade Organisation rules.
"We are studying the contracts on a case-by-case basis to see if they respect WTO rules. All we can do is analyse each of the agreements. The last thing we need now is a row at the WTO," a spokeswoman said.