Bush: Hoping for tighter security against terrorists
Speaking by videolink to 17 eastern and central European leaders meeting in Warsaw, Mr Bush said the al-Qaeda network was trying to export "terror throughout the world".
The European leaders applauded warmly when he thanked them for supporting the US-led campaign against al-Qaeda - which Washington blames for the 11 September attacks in the United States - and the group's Taleban protectors in Afghanistan.
They adopted an anti-terrorism plan including tighter border controls, better coordination of intelligence services and closer scrutiny of the banking sector to combat money laundering.
Many of the 17 leaders are eager to bring their former communist countries into the western military alliance Nato, analysts said.
In other developments
"Al-Qaeda operates in more than 60 nations including some in Central and Eastern Europe. These terrorist groups seek to destabilise entire nations and regions," Mr Bush said.
"They're seeking chemical, biological and nuclear weapons. Given the means, our enemies would be a threat to every nation and eventually, to civilisation itself."
'With us or against us'
Speaking at the White House later after meeting French President Jacques Chirac, Mr Bush said he was unsure whether Bin Laden and his al-Qaeda organisation already had such weapons.
"He announced that this was his intention and I believe we need to take him seriously," Mr Bush said.
"A coalition partner must do more than just express sympathy," Mr Bush said. "A coalition partner must perform."
But he did not single out any country for failing to support the US-led campaign.
Mr Chirac pledged continued French support, but opinion polls show growing doubts about the military action in Afghanistan among the French public.
The BBC's Central Europe correspondent Ray Furlong says world leaders are concerned that eastern and central Europe does not become the continent's "soft underbelly", vulnerable to terrorist penetration.
Money-laundering fears
Eastern Europe is also featuring in the investigation into the 11 September attacks on America.
Poland has revealed that suspects in the attacks on the World Trade Center travelled across its territory, and the Czech Republic has said that Mohammed Atta, suspected of piloting one of the hijacked planes, met an Iraqi agent in Prague.
There are also fears about the region being used for money-laundering, and as a route for drug-smuggling.
Support falling
Some east European leaders have said the 11 September attacks underline the need for the accelerated entry of their countries into Nato and the European Union.
Mr Bush said he stuck to his vision of Europe as a "house of freedom" - outlined in a visit to Poland earlier this year.
Continued expansion of Nato and the European Union were part of that vision.
Latest opinion polls in Poland show support for military action is falling.
Only 30% would favour sending their troops into Afghanistan, compared to 60% immediately after the attacks on the US.
So far, the Czech Republic is the only country in the region that says it is preparing forces for action - an anti-chemical warfare unit.