Georgia, a US ally, considered the move Russian aggression against its territory, as did the US. Russia believed the US was meddling in its sphere of influence.
Relations between the US and Russia have improved in recent months, with Dmitry Medvedev, the Russian president, visiting Washington for a friendly meeting with Barack Obama, his American counterpart.
'Reset' in relations
Obama said he wanted to "reset" relations with Russia and those overtures seem to have gained traction in Moscow, Russia's capital.
Andres Fogh Rasmussen, Nato's secretary-general, has asked Russia for more help in Afghanistan, where the Soviet Union lost 15,000 troops fighting western-backed mujahideen insurgents before withdrawing in 1989.
Makarov, chief of Russia's armed forces general staff, said that Russia was pursuing a possible deal to supply Nato helicopters, but gave no further details.
"We are working on the question related to the helicopters as they are needed in Afghanistan. So this set of questions is at the stage of being decided," he said.
"The long-term interests of Russia and the alliance coincide in this region."
Russia had previously agreed to provide transit routes for Nato members shipping cargo and personnel into Afghanistan.
Di Paola said that in the next few months, the Nato alliance would focus on preparing a programme of joint actions with Russia for 2011.
Nato sees more scope for co-operation in logistics, such as air-to-air refuelling and heavy-lift air transport, and wants to start a programme next year to swap air traffic data.