In their joint declaration, the two leaders called on all countries to join a global coalition for fighting international terrorism.
Mr Putin and Mr Bush believe that Russian-American cooperation is a key element in global efforts directed against terrorism.
Vladimir Rushailo, Secretary of the Russian Security Council, and Condoleezza Rice, the US President’s national security advisor, took part in the meeting.
Later, the two leaders held a joint news conference on the results of the meeting.
The Russian President described his meeting with the US President as useful and constructive. He expressed hope that Russia and the United States would reach an agreement on the Anti-Ballistic Missile Treaty with respect to national interests of the both countries and the need to strengthen international stability in this important sphere.
At the same time, Mr Putin stressed that for Russia, the Anti-Ballistic Missile Treaty is the most important element of the world’s stability.
A working dinner closed the meeting between President Putin and President Bush.