'One Cold War enough'
The former US intelligence director said: "We all face many common problems and challenges that must be addressed in partnership with other countries, including Russia."
He went onto say he had accepted an invitation from Putin - a former employee of the KGB during the Soviet era - to visit Russia.
Putin offered some of his harshest comments against the US during his seven years in power, on Saturday, attacking the concept of a "unipolar" world, dominated by Washington.
"The Americans need to realise there is no free breakfast. As long as they ignore Russian interests, Russia will intervene"
Aleksandr Pikaev, Committee of Scientists for Global security
His remarks came amid continuing disagreement between Russia and the US over the Iraq war and the nuclear ambitions of Iran and North Korea.
Gates, who studied the Soviet Union and Russia as a career CIA analyst, also raised concerns on Sunday about Russia's arms transfers and "its temptation to use energy resources for political coercion" - policies he said could threaten international stability.
"One Cold War was quite enough," he said.
Aleksandr Pikaev, from the Moscow-based committee of scientists for global security, said Russia is reacting to US deeds.
"His [Putin's] speech was not a sickness, it was a symptom of a disease that already exists.
"There are disagreements between the US and Russia, and there are many areas in which they overlap.
"I suspect he will stay on and for that reason he needs to project himself as a hard-line man, protecting Russia's interest"
Aleksandr Nekrassov, former adviser to president Boris Yeltsin
"The Americans need to realise there is no free breakfast. As long as they ignore Russian interests, Russia will intervene. Iran is one issue for instance.
"I expect Russia will take more steps the US won't like."
'Public relations offensive'
John McCain, a US senator, said to the conference: "I remain concerned about the long term possibilities of Moscow's foreign police and energy policies."
"Today's world is not unipolar."
Aleksandr Nekrassov, former adviser to president Boris Yeltsin said that Putin is on a "public relations offensive" because of the ensuing 2008 presidential elections in which many think he will stay on for a third term.
"I suspect he will stay on and for that reason he needs to project himself as a hard-line man, protecting Russia's interest."