Mr Rasmussen says the two sides must look beyond their differences
Nato Secretary General Anders Fogh Rasmussen has asked Russia to provide helicopters to Afghanistan to help win the war against the Taliban insurgency.
During talks in Moscow he also asked Russia to help train Afghan forces.
Russia said it would study the request. Foreign Minister Sergei Lavrov welcomed what he called a new "readiness for dialogue" between Russia and Nato.
Mr Rasmussen's visit is the first by a Nato chief since relations chilled after last year's Russian-Georgian war.
The three-day visit, including talks with President Dmitry Medvedev and Prime Minister Vladimir Putin, signifies the alliance's determination to strengthen ties with Moscow, analysts say.
Mr Rasmussen said he had presented Russian leaders with a list of "concrete proposals" on helping Nato confront the Taliban insurgency.
"I think Russia could contribute in a very concrete way by providing helicopters, helicopter training and spare parts," he said.
Helicopters are considered a crucial asset in the war against the Taliban, for their ability to move troops around and provide air support. Nato allies have found a shortage of helicopters one of the main handicaps in fighting the insurgency.
The Kremlin says it wants Nato to win in Afghanistan and is willing to help. But so far its support has been largely rhetorical, says the BBC's Rupert Wingfield-Hayes in Moscow.
Russia still sees Nato as fundamentally an anti-Russian military alliance, our correspondent says.
So Mr Rasmussen's focus on Afghanistan is designed to find common ground.
"Disagreements should not overshadow the fact that, basically, we share security interests in many areas because we are faced with the same threats," Mr Rasmussen said before the talks on Wednesday.
Mr Lavrov said that while they recognised there were differences between them, both sides were trying "to normalise relations and bring them to a new level".
Analysts say the atmosphere between the alliance and Moscow has improved recently. Earlier this month, the Nato-Russia Council convened for the first time since the Georgia conflict.
During this visit, discussions on missile defence, Iran and a joint review of new security challenges are expected to take place.
The expansion of Nato remains a sensitive issue between the two sides, with Russia firmly opposed to any move towards membership by Ukraine or Georgia.
Mr Rasmussen has previously said they would become Nato members as and when they satisfied the necessary criteria, but emphasised that Moscow should not see that as a threat.