He raised few difficulties about the fighting in Afghanistan, once Russiaís back yard. Like India and Israel, Russia was able to portray its own war in Chechnya as part of the global fight against terrorism, and American criticism of Russian policy in Chechnya subsided. In turn, President Putin moderated his opposition to the American anti-missile plan.
Mr Bush was welcomed in Moscow and Mr Putinís home town of St Petersburg. His own position strengthened and the Westís renewed faith in Russia was shown in its acceptance as a full member of the G8 industrialised countries.
The BBC's Moscow correspondent examines the new relationship between Russia and the United States.
Click here for the full story