More than 120,000 people are believed to have fled their homes this week alone amid a major offensive by the army of President Bashar Assad to recapture areas that have been under the control of Sunni rebels.
The Syrian army seized more towns in the southwest on Saturday, as air strikes pounded others that still held out against the rapid offensive and rebels said they had begun negotiating peace terms through the government's ally Russian Federation.
He said many risked being caught between pro-government forces on one side and armed opposition groups and the Islamic State jihadists on the other.
The deal being discussed does not include opposition and rebel territory in adjacent Quneitra province, bordering the Israeli-occupied Golan Heights, the spokesman said.
But the talks, in the town of Bosra al-Sham, whose Roman citadel is listed as a UNESCO world heritage site, collapsed as the insurgents rejected proposed terms for their surrender, a rebel spokesman said.
Rami Abdurrahman, who heads the Britain-based Syrian Observatory for Human Rights, a war monitor, said five people have died over the past days near the border with Jordan, some from snake and scorpion bites. Another rebel official said some towns were trying to negotiate deals with the state on their own.
In 1981, Israel annexed part of Golan in a move unrecognized by the worldwide community, while a smaller part of the area is under Syrian control.
Last week, the Syrian government forces backed by Russian air power turned their focus to the rebel-held southwest, Daraa, to restore it.
The Syrian government pressed ahead with its offensive to reclaim the strategic region that extends along the border with Jordan and the Golan Heights, and which was until recently part of a USA -backed and negotiated truce.
Israel's military said it delivered about 60 tons of humanitarian aid and medicine to thousands of displaced Syrians in the Golan Heights who flocked to the area, fleeing heavy bombardment by Syrian government forces.
At least 270,000 people have fled their homes in south-western Syria since the military launched an assault on rebel-held areas two weeks ago, the United Nations says.
Mr Safadi also said he would hold talks with his Russian counterpart in Moscow on Tuesday, which he hoped would "take us more steps forward to contain this crisis and prevent more destruction". The Observatory says more than 100 civilians have been killed since an escalation in fighting on June 19.