The campaign, which has already restored Assad's control over a critical portion of the frontier with Jordan, marks another milestone in his efforts to recover control of the country fractured by more than seven years of conflict.
With a mix of military power and negotiated surrenders, his forces this month captured more than 90 percent of Daraa, the southern province where protests against him first erupted in 2011.
Air strikes also hit opposition areas in Quneitra that lie within four kilometres from the sensitive buffer zone with the Israel-annexed Golan.
It comes after a week of heavy artillery shelling and air strikes from Syrian and Russian forces on Nawa, according to the United Kingdom based Syrian Observatory for Human Rights (SOHR).
Syrian President Bashar Assad said Sunday the success in driving the opposition out of Daraa embodies the will of his army and allied forces to "liberate all of Syrian territories" of "terrorism".
The deal, according to the Observatory, does not include Hayat Tahrir al-Sham, a jihadist-led alliance that holds territory straddling the provinces of Quneitra and neighbouring Daraa.
A rebel negotiator confirmed a preliminary ceasefire agreement on Quneitra had been reached with Moscow but said it was unclear when it would be implemented.
Israel passes 'racist' nation state law
The bill has bitterly divided Israeli lawmakers, with some arguing that the law will institutionalise "apartheid" rule in Israel. Lawmakers took turns to passionately express their views in a rowdy, hours-long debate in parliament overnight.
In a briefing with Israeli reporters, he said Israel had not had a problem "with the Assad regime for 40 years", noting that "not one bullet was sacked on the Golan Heights" in that time.
Israel has been on high alert in recent weeks amid the spike in hostilities in the south.
US President Donald Trump announced earlier in the week after meeting Russian President Vladimir Putin that Washington and Moscow had agreed to coordinate efforts in order to ensure Israel's security.
It says its main priority is preventing its archfoe Iran, a key backer of Assad, from building up its military installations in Syria.
Late Sunday, a military source accused Israel of bombing a government position in Aleppo province to help rebels in the south.
Towns near the border area of Syria in the Golan have been under heavy bombardment from pro-Assad sources that are said to be backed by Russian Federation.
Besieged for three years by rebels and HTS, the Shiite-majority towns had become a rallying cry for the government and Iran, another key regime ally.
Trump blames Putin personally for election meddling in latest reversal
One user said Melania "was the only one in the room who understands how risky this man actually is", referring to Putin. A USA diplomat, who wished not to be named, told the Daily Beast that President Trump is nothing but a "p*ssy".
Rebels in Nawa, where tens of thousands of people live, are in talks with Russian Federation for a potential handover deal too, according to the observatory.
The departure was emotional and bittersweet, said Shilan Shuweish, a Fuaa resident who left with her husband and two children.
Hundreds of fighters and some relatives, carrying suitcases packed with clothes, boarded around 15 buses in Daraa city, AFP's correspondent there said.
"Since morning, our units have been steering flaming kites and balloons over Israeli-occupied territory to show that we don't take orders from anyone", the Sons of al-Zawari, a self-proclaimed "brigade" of Palestinian kite flyers, said in a statement released yesterday, according to the Anadolu Agency (AA).
"The offensive has triggered the single biggest displacement of the war, with several hundred thousand people uprooted".
"There are still empty buses in the city and it is unclear if there will be more evacuations", said the head of the Britain-based group, Rami Abdel Rahman.
Trump looks forward to second summit with Putin
He mentioned London-based financier Bill Browder , a onetime investor in Russian Federation who said he exposed corruption there. "Well I would, because he's in charge of the country", he said .