"Russia together with the Syrian government have already announced the establishment of humanitarian corridors in Eastern Ghouta," Lavrov told the UN Human Rights Council.
"Now, it is the turn for the militants and their sponsors to act, militants entrenched there who still continue shelling Damascus, blocking aid deliveries and the evacuation of those wishing to leave," he added.
Tuesday was the first day of the five-hour daily "pause" in rebel-held Eastern Ghouta that was ordered by President Vladimir Putin, the Syrian regime's main ally.
But the truce was marred by violence, with Moscow and Damascus accusing armed groups of shelling the purported humanitarian corridor.
The Eastern Ghouta truce falls far short of a broader 30-day ceasefire Russia agreed to at the UN Security Council on Saturday but which has yet to take effect.
Lavrov said the Security Council resolution could offer reprieve to those suffering across Syria, but indicated the ball was in the court of the opposition and its allies in Washington.
"The people of Syria today face the most dire humanitarian crisis. UN Security Council resolution 2401 has established a framework for all parties to agree upon conditions to alleviate the plight of civilians throughout the territory of the country," he said.
"We call upon the members of the so-called American coalition to ensure the same humanitarian access to the areas in Syria under their control."
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)