"We note the efforts the Taliban is making to stabilize the military-political situation," Lavrov said at the third meeting of the Moscow format of consultations on Afghanistan, Xinhua news agency reported.
However, the lack of international recognition of the Taliban, economic woes and humanitarian challenges illustrate instability in the country, he said.
The minister also pointed to threats from terrorist groups, primarily the Islamic State and Al-Qaeda, and the "acute problem" of drug production.
Lavrov called on the Taliban to prevent anyone from using Afghan territory against third countries, especially against Afghanistan's immediate neighbours.
He urged the international community to provide Afghanistan with effective financial, economic and humanitarian assistance, and the United Nations should play a central coordinating role.
Acting Deputy Prime Minister of the Afghan Taliban's interim government Abdul Salam Hanafi said the Taliban seeks to build good relations with its neighbours and all other countries.
Afghanistan's Acting Foreign Minister Amir Khan Muttaqi said that the current government would not allow its land to be used against other countries.
Representatives from 10 countries attended the multilateral talks in Moscow, and the Taliban delegation was led by Hanafi.