Lavrov spoke in Kazakhstan on Friday, saying the cease-fire will be extended “until all (civilians) leave” the enclave known as eastern Ghouta.
The Russian Defense Ministry said that 2,000 people had exited the rebel-held suburbs by early morning.
Thursday saw the largest single-day exodus of civilians in Syria’s civil war. Tens of thousands emerged from Hamouria and other opposition towns to escape the onslaught.
The civilians were fleeing as Syrian government troops, backed by Russian aircraft, pushed further into eastern Ghouta.
Elsehwere, Turkish forces are pushing their way into the northern Kurdish-held town of Afrin.
