Mr Rasmussen said he had presented Moscow with 'concrete proposals'
Nato Secretary General Anders Fogh Rasmussen has failed to gain any commitment from Russia to help win the war against the Taliban insurgency.
On Wednesday Mr Rasmussen asked Moscow to provide helicopters to Afghanistan and also requested Russian help in training the Afghan air force.
But he told the BBC he had received no positive response from the Kremlin.
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, which has included meetings 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" to help the Western alliance defeat the Taliban in Afghanistan - specifically requesting helicopters, helicopter training and spare parts.
Mr Rasmussen said the two sides should look beyond their differences
"The Russians do realise that if we left Afghanistan behind and if Afghanistan once again became a safe haven for terrorism then they could suffer from it because terrorists would spread from Afghanistan through central Asia to Russia," Mr Rasmussen told the BBC.
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 has said it wants Nato to win in Afghanistan and is willing to help. Russian Foreign Minister Sergei Lavrov said that while differences remained between Moscow and Nato, both sides were trying "to normalise relations and bring them to a new level".
But while many analysts agree it is not in Russia's interests to see Nato fail in Afghanistan, Moscow is still deeply suspicious of the old Cold War alliance, says the BBC's Rupert Wingfield-Hayes in Moscow.
Giving helicopters to a US-backed regime in Kabul goes way beyond what the Kremlin is prepared to do, our correspondent adds.
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, issues such as missile defence, Iran and a joint review of new security challenges were expected to be on the agenda.
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.