"
Our position is not a problem, it is a constructive contribution
"
German Foreign Minister Joschka Fischer
French Finance Minister Francis Mer said he was "profoundly vexed" by Mr Rumsfeld's remarks - which branded France and Germany "old Europe - while a former employment minister described the US as arrogant.
And German Foreign Minister Joschka Fischer said that the word "problem" was inappropriate.
"We should try to treat each other sensibly," he said.
"Our position is not a problem, it is a constructive contribution."
'Old' Europe
Mr Rumsfeld made his remarks in response to a pledge on Wednesday by French President Jacques Chirac and German Chancellor Gerhard Schroeder to work together to oppose war in Iraq.
"Germany has been a problem and France has been a problem," Mr Rumsfeld told Washington's foreign press corps on Wednesday.
"But you look at vast numbers of other countries in Europe, they're not with France and Germany... they're with the US.
"You're thinking of Europe as Germany and France. I don't," he said. "I think that's old Europe."
On Thursday, the French and German leaders reiterated their opposition to war as they continued celebrating the 40th anniversary of the Elysee Treaty between their two countries.
"
Rumsfeld is not exactly a diplomat and it is not very wise to say something like that
"
Former German Defence Minister Volker Ruehe
"We are both of the opinion... that one can never accept it when it is said that war is unavoidable," Chancellor Schroeder said in an address to hundreds of French and German students in Berlin attended by Mr Chirac.
"War may never be considered unavoidable."
A spokeswoman for Mr Chirac called for calm in the dispute.
"Polemics have no place in this debate," Catherine Colonna said.
'Eastward shift'
Mr Rumsfeld expanded on his remark about "old Europe" by pointing to the planned eastward expansion of Nato as far as the three Baltic republics.
"
If you knew what I felt like telling Mr Rumsfeld...
"
Roselyne Bachelot, French Environment Minister
"If you look at the entire Nato Europe today, the centre of gravity is shifting to the east," Mr Rumsfeld said.
But the conservative former German Defence Minister Volker Ruehe, normally a strong US supporter, said it was unfair to play off Eastern and Western Europe against each other.
"Rumsfeld is not exactly a diplomat and it is not very wise to say something like that," he said.
European divisions
The BBC's James Coomarasamy, in Paris, says the divisions between Europe and the US over Iraq are growing more public and the rhetoric more pointed by the day.
The French Environment Minister, Roselyne Bachelot, told one interviewer: "If you knew what I felt like telling Mr Rumsfeld..."
She then stopped herself, saying the word was too offensive.
Europe is deeply divided over the possibility of war with Iraq. France and Germany are opposed to early military action, while the UK is sending massive troop deployments to the Gulf.
US Secretary of State Colin Powell has questioned the commitment of France and Germany to disarming Iraqi leader Saddam Hussein.
However, he has described the disagreements with France as a "blip", saying he hoped "the French would come to the understanding" of the need to use the threat of force to compel Saddam Hussein to disarm.