"We do not think NATO's expansion is necessary, and believe the policy is a relapse into the Cold War," Lavrov told a news conference following talks with his Finnish counterpart.
Lavrov said Europe should instead join efforts in countering the spread of weapons of mass destruction, terrorism and other threats facing all the continent's nations.
Three ex-Soviet Baltic republics and seven former Communist-bloc states in Eastern Europe have joined NATO since the breakup of the Soviet Union. Former Soviet allies Ukraine and Georgia have also declared plans to join the 26-member alliance.
Russia has repeatedly expressed concern about the emergence of new NATO bases close to its borders and the bloc's reluctance to ratify an updated Conventional Forces in Europe (CFE) treaty, which has regulated the deployment of troops and weapons on the continent since the Cold War.
Moscow has dismissed NATO's arguments that it must first withdraw troops from Moldova and Georgia, and has imposed a moratorium on the implementation of the old CFE treaty.
Lavrov said Moscow welcomed cooperation with the bloc within existing formats.
"There are various formats of cooperation between NATO and Russia, or Ukraine or other countries. There are no obstacles to joint work in the future," the minister said.