Lavrov described as "artificial" NATO's timeline for withdrawal from the 10-year war, AP reported.
Lavrov, who attended a meeting of NATO defense and foreign ministers in Brussels, said China and other countries in Asia were also worried about the withdrawal plan.
NATO and Russia on Thursday discussed a plan to give the alliance a new logistics facility on Russian territory for the transfer of military cargo to and from Afghanistan, diplomats said.
NATO and Russia also examined ways of assisting Afghan government forces in their battle with the Taliban insurgency, the diplomats said on condition of anonymity in keeping with regulations.
Moscow has provided NATO with air corridors and railway routes for carrying supplies to and from landlocked Afghanistan. The link has become particularly important since Pakistan blocked NATO supplies from crossing its territory following an alliance airstrike that killed 24 Pakistani border troops in November.
On Thursday, foreign ministers of NATO's 28 members and their Russian counterpart, Sergey Lavrov, were meeting in Brussels to discuss these and other issues as part of their regular consultations.
A new proposal now being considered by Russian lawmakers would for the first time allow alliance members to set up a logistics facility in Ulyanovsk, Russia, for troops and cargo.
Officials said that there were "no differences" between the two sides on the use of the air base in Ulyanovsk.
"We expect to expand the transit options offered to us by Russia ... to Afghanistan," NATO Secretary-General Anders Fogh Rasmussen said after the meeting.
"We appreciate very highly Russia's contribution, which is based on our shared interests and contributes to our shared security," he said.
Moscow views NATO's military effort in Afghanistan as crucial for its own security interests, including helping to prevent instability from spreading into ex-Soviet Central Asia.
But the former Cold War rivals remain sharply at odds over a U.S.-led NATO missile defense plan in Europe that Washington says is aimed at deflecting a potential Iranian threat. Moscow fears it will eventually become powerful enough to undermine Russia's nuclear deterrent.
Despite those differences, Russia has also cooperated with the alliance in suppressing piracy off the Somali coastline and in such areas as anti-terrorism, counter-narcotics and search and rescue at sea.
Source : Afghan Voice Agency (AVA), International Service