This comes after reports that Russian air strikes had targeted southwest Syria for the first time in four days, hitting the rebel-held towns of Tafas and Saida.
The refugees are heading to the borders with Jordan and the Israeli-occupied Golan Heights, but neither country is willing to accept them.
Israel's military deployed tank and artillery reinforcements to the Golan on Sunday, a statement said, "in light of developments on the Syrian Golan Heights".
At the meetings with Russian Federation, rebel negotiators sought a deal for all of Daraa province to come back under government sovereignty, but without the army or police entering the area, an insurgent spokesman said.
The proposal for the Nusra Front was their evacuation to rebel-held areas in northern Syria, said the observatory, adding that the leader of the group in Daraa rejected the evacuation proposal and called for a general mobilization to fight the government forces till the end.
Talks in Syria between opposition forces and Russian regime allies broke down Wednesday with no further sessions having been set, according to rebel spokesperson Ibrahim Jabbawi.
The state media said the military operations are going in tandem with the reconciliation efforts, which explains the situation where several towns accepted the entry of the Syrian army without battles.
Through military operations and those deals, Syrian troops are now in control of more than 60 percent of the southern province of Daraa.
A week ago the global organisation said that 160,000 people had been displaced.
Eleven members of a single family were killed overnight in a land mine blast as they returned to Al-Mseifra, which had "reconciled" with the government, the Observatory said Wednesday.
On Thursday, Amman expressed readiness to help the United Nations assist displaced Syrians, but without going so far as to open its border.
Safadi said Amman keeps open channels with Damascus and Moscow and that his talks with Lavrov will focus on reaching a cease-fire and halting the displacement.
Sweden, which holds the rotating Security Council presidency, requested the closed-door meeting along with Kuwait.
An estimated 270,000 people have fled air and ground attacks over the past two weeks, the United Nations said on Monday.
Following talks with his Jordanian counterpart Ayman Safadi, who arrived in Moscow on a working visit, Lavrov said the U.S. can rarely separate terrorists and other foreign-backed opposition militants in Syria's southern de-escalation zone.
Safadi called for a ceasefire in the south, saying the developing situation was of "great importance" to Jordan.
Jordan and Israel have said their borders would remain closed, even as tens of thousands of Syrians flee the government offensive.
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