Bush made the call on Wednesday at the end of the annual US-EU summit in Washington.
"I urge the leaders in Europe, and around the world, to take swift and decisive action against terror groups such as Hamas, to cut off their funding and support as the United States has done," Bush said at a joint press conference with EU leaders.
The European Union distinguishes between Hamas's military operations which Washington claims are "terrorist" activities in the occupied West Bank and Gaza Strip and the group's political and social role there.
Washington lists Hamas, which is spearheading the intifada or uprising against Israel's occupation as a "foreign terrorist organisation", a charge the group denies.
Time magazine this week said Washington had accused France of allowing Hamas supporters to raise funds on its territory.
But French embassy spokeswoman Natalie Loiseau said Washington had not sent any formal request to Paris.
Elliot Abrams, a National Security Council Senior Director, brought up alleged Hamas funding at a presentation for diplomats from European countries this month, said diplomats.
“He had some strong language on Hamas but it was not in the form of a formal demarche,” said one diplomat.
French Foreign Minister Dominique
de Villepin said Hamas was a
necessary peace partner
Within the European Union, Britain has taken the US position on the political wing of Hamas against France.
At a meeting in Luxembourg last week, British Foreign Secretary Jack Straw urged his EU colleagues to ban the group.
French Foreign Minister Dominique de Villepin said Hamas was a necessary player in the peace process.
A senior US official, briefing reporters on the EU-US summit, said Washington hoped the 15-nation bloc would take a tougher stance on the Palestinian organisation.
One US official, who asked not to be named, said the US embassy in Paris had tried to discourage confrontation on the Hamas issue, but the Bush administration dismissed these calls.
Washington has also pressured EU leaders to adopt the US policy of sidelining Palestinian President Yasser Arafat. Most EU governments have not heeded the calls.