Around 270,000 people have fled their homes since the Assad regime and its allies began their assault on the southern province of Deraa on June 19, according to the UN High Commissioner for Human Rights (UNHCR).
"A new expanded negotiating committee that represents all the south has been formed to reach an agreement to spare innocent lives and ensure the safety of civilians and fighters", said a statement by the central operations room in the south, representing the key rebel factions in that region.
Around 164,000 of the displaced people are now close to the Golan heights - an area of Syria now occupied by Israel - while 60,000 are close to the Jordanian border.
The rebels said the talks had failed on Saturday afternoon but the process has since been revived after Jordan stepped in.
Negotiations for settling the situation in Daraa have been ongoing between the Russian side, which is representing the Syrian government, and an array of rebel groups in that area.
It has remained under opposition control since the war began, but as the Syrian government has strengthened its hold on other parts of the country, Daraa has become a new target.
But Moscow had roundly rejected the terms, the source said, and responded with a counter-proposal.
On Wednesday, Human Rights Watch demanded both Jordan and Israel allow asylum-seekers in.
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Some displaced families whose hometowns had fallen back under regime control have been returning, but even that journey is unsafe.
World powers have criticized the operation for violating a ceasefire announced past year by Washington, Amman and Moscow, but they have not managed to halt the blitz.
Sweden, which holds the rotating Security Council presidency, requested the closed-door meeting along with Kuwait, Swedish diplomats said Tuesday, July 3.
The Syrian army is fighting the rebels, including the Islamic State (IS) and the Nusra Front, in the countryside of Daraa, as well as the in the countryside of the nearby province of Sweida and the Quneitra province near the Israeli-occupied Golan Heights.
Jordanian Foreign Minister Ayman Safadi said on Wednesday dozens of trucks are waiting for Syrian permission to supply humanitarian aid from Jordan to Syria.
Safadi called for a ceasefire in the south, saying the developing situation was of "great importance" to Jordan.
In the meantime, a major insurgent-held town in southwestern Syria has accepted the return of regime leader Bashar al Assad's rule, pro-regime media and a war monitor said on Sunday, though some local activists and rebels disputed a deal had been completed.