Russian guarantees will also be extended to rebel fighters who wish to "settle their status" with the government - a process by which former insurgents accept to live under state rule again, the rebel sources said.
Assad's next target in the south-west appears to be rebel-held areas of Quneitra province at the frontier with the Israeli-occupied Golan Heights, where fighting between insurgents and the government escalated on Friday.
Smoke rises above rebel-held areas of the city of Daraa during reported airstrikes by Syrian regime forces on July 5, 2018.
However, a state television correspondent said the surrender talks in Deraa were continuing, and no final deal had been reached because of differences between the rebel groups.
Syrian government forces have taken over the southern Nassib crossing on the border with Jordan as rebels agreed to give up their weapons in a deal with Russian Federation, marking a major victory for Syrian President Bashar Assad.
Rebels in besieged areas of southwestern Syria say they are returning to negotiations with Russia over a possible pullout after an intensive bombing campaign by Russian and Syrian forces.
Rebels then handed some 275 square kilometers of territory near the border to government forces without a fight, said observatory chief Rami Abdel Rahman.
The Israeli Defense Forces (IDF) have attacked an outpost of the Syrian Army near the occupied Golan Heights after shells flew across the border.
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Friday's agreement came after bombardment of rebel-held areas intensified earlier this week after rebels rejected a deal with the Russians.
The commander in the pro-Assad alliance told Reuters the army and its allies had seized a string of villages and reached the border.
Rebels in southern Syria said on Friday they were close to reaching a deal with regime ally Russian Federation including a ceasefire and the handover of some territory.
The fighting and air strikes have already driven more than a quarter of million people in southwest Syria from their homes, the United Nations said on Monday, seeking shelter along the frontiers with Jordan and Israel.
The UN children's agency, UNICEF, said in a statement on Friday that it received "horrific reports" of an entire family including four children being killed.
Syrian army soldiers managed to establish full control over a strategic town in Dara'a, as they seek to put an ultimate end to the presence of militants in the eastern and southeastern sectors of the province.
The Observatory said Syrian troops were now about three kilometers (2 miles) from the Naseeb border crossing.