Meeting in the Slovak capital Bratislava, they also said they will speed up negotiations on Russia's entry into the World Trade Organization (WTO).
Putin said during a joint news conference after the summit that Russia is committed to the fundamental principles of democracy.
Bush said he raised the issue of democratic ideals in Russia during their meeting. Putin was then asked about criticisms that Russia is becoming less democratic than it was before he came into office.
Putin said Russia made its final decision in favor of democracy 14 years ago and "there can be no return." He said that "any kind of turn toward totalitarianism would be impossible due to the condition of Russian society."
Bush said they agreed to enhance cooperation to counter the threat of nuclear terrorism.
The two leaders issued a statement during their summit in Slovakia that they instructed their trade ministers to accelerate bilateral negotiations to complete talks on Russia's WTO entry this year.
The statement also said they agreed to enhance cooperation to counter the threat of nuclear terrorism, a point that both leaders stressed at a joint news conference following their meeting.
The Kremlin press office said today that U.S. Secretary of State Condoleezza Rice and Russian Defense Minister Sergei Ivanov signed an agreement in Bratislava to curb the spread of shoulder-fired missiles in order to fight terrorism.
(AP/AFP/Reuters/CTK)[For more on the Russia-U.S. summit, see RFE/RL's dedicated Bush-Putin Summit 2005 webpage.]