NATO Secretary-General Anders Fogh Rasmussen met President Dmitry Medvedev at the Kremlin to iron out a new bilateral agreement to be signed at a summit of the 28-nation alliance in Lisbon on 19-20 November.
Relations are "becoming more productive and substantial," Medvedev said. "This gives an opportunity to [...] create a more robust security system in Europe and the world."
The United States considers NATO cooperation with Russia crucial to President Barack Obama's plans to "reset" relations, which sank to a post-Cold War low during the presidency of George W. Bush and Moscow's 2008 war with pro-Western Georgia.
"The meeting in Lisbon is a real opportunity to turn a new page, to bury the ghosts of the past," Rasmussen told Russian journalists.
Despite the warm words, the two sides offered little detail about the agreement, which Russia wants to define more clearly NATO's role in Europe and its missile defence plans, and which NATO wants to include concrete assistance to its Afghan mission.
Russian and US officials last week hailed an unprecedented joint anti-narcotics operation in Afghanistan as a result of efforts to improve strained relations. Rasmussen said he wanted to see more of these in the future.
Moscow has also agreed to sell the US Navy 21 Russian-made Mi-17s - a transport helicopter that can be armed with guns and rockets - for use in Afghanistan.
"We will continue to expand our cooperation on Afghanistan. It is in our fundamental interest," Russian Foreign Minister Sergei Lavrov told Rasmussen after holding brief talks.
Lavrov did not give details of what more Russia planned to do to help NATO fight drug trafficking in Afghanistan or whether it would expand supply routes, which NATO has sought as an alternative to insecure trucking routes over Pakistan.
NATO has stressed that cooperation will not include the deployment to Afghanistan of troops from Russia, which is still haunted by the defeat of Soviet forces which invaded Afghanistan in 1979 and quit in humiliation a decade later.
Cooperation on missile shield
Russia also said it would be willing to cooperate on a NATO-proposed European missile defence system to counter what NATO sees as a potential threat from Iran - something Moscow had feared could negate its own strategic arsenal.
"We are willing to take part in such a joint system and a joint analysis [...] Of course, on an equal basis and aimed against joint threats," Lavrov said.
Bush administration plans to site elements of a shield in Poland and the Czech Republic were a major bone of contention, until Obama agreed to scale back the plans.
It was unclear whether Rasmussen would speak with Prime Minister Vladimir Putin, seen as Russia's key decision-maker.
Russian cooperation on Afghanistan would be an important victory for Obama, weakened by Tuesday's mid-term elections in which Republicans captured control of the House of Representatives from the Democrats.
Many officials in Moscow still view its old adversary NATO with deep suspicion and experts say a complete thaw in relations could take some time.
(EurActiv with Reuters.)