The zone where the ceasefire was declared had seen "a rapid fall in the level of violence", Lavrov said in Brussels.
Russia hoped that trend would continue and that the ceasefire zone would be extended at the next cycle of Syria peace talks in Kazakhstan next month, he added at a news conference with Belgian Foreign Minister Didier Reynders.
The truce, which was brokered by Russia, the United States and Jordan, has been in force since Sunday in the provinces of Daraa, Quneitra and Sweida.
They are Idlib in the northwest, the central province of Homs and the rebel enclave of Eastern Ghouta on the outskirts of Damascus.
Sunday's ceasefire went into effect just ahead of the start of the latest round of UN-brokered peace talks in Geneva, which are being held in parallel with the diplomatic efforts in Astana.
More than 3,20,000 people have been killed in Syria since the conflict began in March 2011 with anti-government protests.