Answering questions in an Internet Web cast, Putin also called President Bush "a decent person" and a good partner, "with whom it is possible not just to talk but to reach agreement."
He said he had sent greetings to Mr. Bush on his 60th birthday.
"As a human being, (Bush is) one of the people I consider to be my friends," he said, speaking before a summit of the Group of Eight leading industrialized nations that he will host July 15-17 in St. Petersburg.
Pressed to name Russia's chief enemies, Putin said he hoped that "terrorists and drug barons" would become the only main foes of leading nations.
But while he stressed cooperation with the United States, the Russian leader indicated that Moscow's former Cold War foe should not dominate the post-Soviet world, saying that because the planet is diverse, "it should be multipolar."
With oil prices high, Putin has been seeking to boost energy-rich Russia's global clout.
Putin also said the war his government has waged against separatists in Chechnya has been "worth it," asserting that militants wanted to create a separate state stretching from the Black Sea to the Caspian.
Defending a widely criticized referendum that cemented Chechnya's status as part of Russia, Putin suggested similar votes could be held in breakaway provinces in neighboring Georgia and called for unified global standards for determining the status of separatist regions such as Kosovo in the Balkans.
Also Thursday, Putin answered what was for many observers a more burning question: What compelled him to kiss the bare stomach of a young boy