President Jacques Chirac has said France will join the US and Britain in the fight against terrorism, suggesting that French forces could play a direct role in the military offensive.
Canada and Australia also committed themselves to military support, while the German Chancellor, Mr Gerhard Schr÷der, said his country would join the military action if requested.
"In recent days, the United States made new demands for military participation," Mr Chirac said in a brief address on national television yesterday.
"We will assume our role in the spirit of solidarity and responsibility," he added, without elaborating.
"The fight against terrorism is complex and without mercy. The military operations will take place over a long period."
Mr Chirac said they were aimed at "punishing the guilty and destroying the infrastructure of the terrorist network and their support in Afghanistan".
Mr Schr÷der said German troops had not participated in the US-led strikes in Afghanistan on Sunday but he renewed his pledge to aid the US in military action if needed.
Mr Schr÷der, flanked by Foreign Minister Mr Joschka Fischer, told a news conference that Germany's solidarity with the US was "unlimited" and "did not exclude a military contribution if it is requested.
"Until now, we have received no such concrete demand."
The head of the German government declined to speculate on when the country might be asked to take part in military action and what type of assistance could be given.
Mr Schr÷der said Germany was committed to the fight against terrorism and that there was "no alternative to this conflict that we must win and will win".
He added that the military action should not be seen as a war on the people of Afghanistan or Islam but against terror.
"We did not want this confrontation," he said. "It is international terrorism that has imposed it on us."
In his address to the nation, President Bush said that British forces participated in the operation and that other allies, including Canada, Australia, Germany and France, had pledged to contribute as the action unfolds.
Mr Schr÷der had said earlier in a statement that the German government supported "without reservation" the US-led attacks on "terrorist targets in Afghanistan".
He added that Mr Bush had informed him beforehand by telephone that the strikes were imminent.