Lavrov made the remarks in a joint news conference in Kabul Monday alongside his Afghan counterpart, Rangin Dadfar Spanta.
Lavrov also said Moscow has invited Afghanistan and its neighbors Iran and Pakistan to a regional security conference in the Russian capital later this month.
The foreign minister's visit to Afghanistan comes as Russian President Dmitri Medvedev seeks to reassert Russian influence in Central Asia. Russia is allowing non-military U.S. supplies bound for troops in Afghanistan to pass through Russian territory by train. Moscow also has struck an energy deal with Uzbekistan and offered Kyrgyzstan about $2 billion in aid and loans.
The Soviet Union invaded Afghanistan in 1979, and Western-backed Afghan fighters forced the Soviets from the country two decades ago.
A senior U.S. lawmaker who recently visited Afghanistan, House of Representatives Speaker Nancy Pelosi, has said that Afghan instability poses a regional challenge requiring the involvement of Pakistan, Iran, Russia and other nations. And U.S. Secretary of State Hillary Clinton said she and Lavrov discussed Afghanistan and Iran when they met earlier this month in Geneva.
Some information for this report was provided by Reuters.