"For its part, the Israeli military, using loudspeakers, asked the Syrians to return to the Burayqah camp; in turn, the Syrian civilians moved back without any incident".
Government troops are also seeking to advance on another town to the south through negotiations with rebels there.
The clashes left 18 regime forces and 13 rebels and allied Daesh members dead, the monitor said.
An AFP photographer there saw a plume of smoke emerging from the sloping hilltop overlooking agricultural plains on Monday.
According to the Agency, Syrian rebels still hold a narrow section, separating the province of Dar al-Quneitra, despite the grip of government forces with the support of Russian Federation the most part of Dar.
The regime's recapture of Daraa city would be a huge propaganda win for Syrian President Bashar Assad as the seven-year uprising against him has its roots there. The American involvement in Syria has mainly been focused on the eastern half of the country, where the Islamic State terror group established the capital of its so-called caliphate in the Syrian city of Raqaa.
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 Syrian government reached a reconciliation agreement Wednesday with rebels in Nawa, in southern Daraa province.
Israeli parliament to vote on contentious Nation State bill
Israeli Prime Minister Benjamin Netanyahu attends the weekly cabinet meeting at his office in Jerusalem on July 15. Long live the state of Israel'. "The Palestinian people will remain the sovereign of this land".
The official news agency SANA said on Sunday Daraa's rebels released five men they had been holding hostage into regime custody, and also surrendered more heavy and medium weaponry.
Reuters first reported the pleas of civilians stranded near the border, which was later confirmed by Syrian humanitarian workers in the area of Quneitra.
The group is among tens of thousands of Syrians who have arrived near the frontier over the past month following renewed fighting along the country's southern Deraa and Quneitra provinces.
Lama Fakih, deputy director of the Middle East and North Africa division at Human Rights Watch, said both the Israeli and Jordanian governments have an obligation to not push back fleeing asylum seekers.
Israeli Cabinet Secretary Tzachi Braverman speaks to Israeli Prime Minister Benjamin Netanyahu as they attend the weekly cabinet meeting at Netanyahu's office in Jerusalem, July 15, 2018.
It was not immediately clear whether the strikes were carried out by the Syrian government or its Russian ally, the Britain-based monitor said.
Iran, which backs Assad against the mainly Sunni insurgents and has expanded its military role in Syria, has long taken an interest in the fate of its co-religionists in the two towns.
On Sunday, Syrian state media reported on an airstrike against the T-4 airbase in the Homs countryside, attributing it to the Israeli Air Force. Israel has refused to grant asylum to citizens of Syria, with which it is technically at war.