Meanwhile, air raids meanwhile intensified, said the monitor, the Syrian Observatory for Human Rights, as displaced people flocked to the border areas least likely to be hit, and the United Nations warned of a humanitarian catastrophe.
Tens of thousands of Syrians have fled since the beginning of the offensive, and the Syrian Observatory for Human Rights monitoring group says that almost 100 civilians have been killed.
The southwest was an early hotbed of the uprising against President Bashar al-Assad and defeat there would leave rebels with just one remaining stronghold - the area around Idlib province bordering Turkey in the northwest.
The UK-based war monitor said at least more eight towns surrendered on Saturday under deals brokered by Russian Federation with local officials and fighters.
On Saturday, the monitor said at least eight battered opposition-held towns in southern Syria had returned to regime control under Russian-brokered deals after almost two weeks of bombardment.
Insurgent negotiators had held meetings with Russian Federation to try to agree on a deal for all of Deraa province to come back under government sovereignty, but without the army or police entering the area.
"We will continue to preserve Israel's security interests and, as always, we are prepared to provide any humanitarian aid to women and children, but we will not accept any Syrian refugees into our territory", he wrote.More news: When Trump meets Putin, United States News & Top Stories
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The regime wants us to hand over everything - Daraa city, the Nasib crossing, ourselves and the heavy weapons.
"[He] calls on all parties to respect their obligations under global humanitarian law and human rights law, protect civilians and facilitate safe, unimpeded and sustained humanitarian access". "It's inadmissible", said a negotiator in the rebel-held part of Daraa city.
The UN refugee agency said on Friday that the number of displaced people in southern Syria had more than tripled to 160,000 in the latest fighting.
Syria's southwest is strategically sensitive because of its proximity to the frontiers with both Jordan and the Israeli-occupied Golan Heights.
In Washington, a State Department official said the United States could not confirm the truce report, and the situation in southern Syria remained "grim" with Russian Federation and Syrian government forces continuing to bomb the area.
In the Syrian province of Deraa in the south-west of the country, Syria's government army continues the operation against groups of terrorists. The Observatory says more than 100 civilians have been killed since an escalation in fighting on June 19.