A major rebel-held town in southwestern Syria has accepted the return of President Bashar al-Assad's rule, pro-government media and a war monitor said on Sunday, though some local activists and rebels disputed whether a deal had been completed.

Losing Busra al-Sham, a major town near the provincial capital of Daraa, would be a significant loss for the opposition in the teeth of a Russian-backed Syrian army offensive in the southwest that has taken chunks of rebel territory.

Jordan on Sunday mediated a new round of talks between rebels and Assad's main ally Russia, seeking a wider truce in the area to avert more bloodshed and another wave of displaced people near its border.

The Syrian Observatory for Human Rights said rebels in Busra, east of the provincial capital Daraa, had agreed on a deal and were handing over heavy weapons.

Activists distributed footage of armoured vehicles being handed to Russian troops, though some local sources said it was a goodwill gesture as talks went on, rather than a sign that a surrender deal was being implemented.

Negotiations between Russia and rebels in the southern town had restarted, the rebels said earlier Sunday, after Jordan stepped in as the mediator.

Talks had collapsed on Saturday as pro-Syrian government forces, backed by Russian air power, took a string of towns and villages in their fresh offensive against rebel-held areas of Syria's south.

The Syrian and Russian air forces have stepped up bombing on southern Daraa province since 19 June. In the face of the intensified bombings and ground assault, rebel lines have collapsed in some areas.

Negotiations with rebels in Busra and Russia collapsed on Saturday amid what the rebels called humiliating demands.

Still, on Sunday morning, spokesman for FSA negotiators Ibrahim al-Jabawi said talks with the Russians had resumed in the historic town.

Busra al-Sham is the location of a famous Roman theatre, a location of great archaeological significance and a UNESCO World Heritage Site.

South Syria: Assad artillery damaged best preserved Roman Theatre in Middle East, located in Bosra and part of UNESCO World Heritage. Airstrikes currently hitting the town. pic.twitter.com/dXitVnRH2z — Lucifuge Rofocale (@rofoca_lucifuge) June 30, 2018

"The talks have resumed this morning between the Russian side and the opposition in southern Syria under Jordanian auspices," Jabawi said.

Jordan is attempting to mediate between the rebels and the Russians, concerned about a possible new wave of displacement in Syria’s south.

The kingdom already holds more than 600,000 officially registered Syrian refugees but says the real number could be as much as 1.3 million and that it cannot take in any more.

More than 160,000 people have already been displaced by the Daraa offensive, and with Jordan firmly refusing to take them in, those fleeing have gathered along the Jordanian border and near the Israeli-occupied Golan Heights.

At least 132 people have been killed in the offensive so far.

Israel said on Sunday it had deployed additional tank and artillery units to the Golan, concerned about the intensified fighting.

Unhappy with restricting itself to mediation, some Jordanians have taken to social media to pressure their authorities into accepting displaced Syrians, using the hashtag "open the borders".

As of Saturday, the Syrian government had control over around a half of Daraa province, up from around 30 percent before the assault, according to UK-based activist group the Syrian Observatory for Human Rights.

Meanwhile, Russia said it shot down an unidentified drone near its Hmeimeem air base in northwestern Latakia province.