Russia has previously allowed non-lethal supplies from European nations for Afghanistan to cross its territory, and recently said the US could follow suit.
"Non-military transit has already been granted as part of our agreements with Nato, and the United States very recently received our agreement... for delivery of their cargoes for the needs of the international forces," Lavrov said.
"Additional steps are also possible," he said in response to whether Russia would also agree to include weapons or other lethal cargo.
"What`s important is that relations between Russia and Nato return to a normal course," he said, in a reference to Western criticism of Russia`s military actions in Georgia last year.
Talks between Russia and Nato have resumed in recent weeks, after they were suspended in reponse to the war in Georgia.
The Nato-led force in Afghanistan is seeking alternative transit routes into the country after an increase in attacks on supply lines in Pakistan.
Lavrov`s comments also come after Kyrgyzstan announced it would close a key US air base on its territory, which was used to help supply operations in Afghanistan.
They also come as Barack Obama, the US president, plans to deploy an additional 30,000 troops to Afghanistan.
Neave Barker, Al Jazeera`s correspondent in Moscow, said Russia`s latest move "signifies a thaw in relations between Russia and Nato, and an increased level of co-operation between Moscow and the new Obama administration".
He said both Russia and US are looking for concessions from each other.
"Moscow is also acutely aware that the failure of Nato in Afghanistan could mean the destabilisation of countries to the north - those post-Soviet nations that still have strong political and economic ties with Russia," he said.