Rebels and other groups still control 70 per cent of Quneitra, while the Syrian government is in full control of Sweida - a third southern province - the Observatory added.
The violence is taking place around 4 km from the line marking the start of the United Nations Disengagement Observer Force zone, an area monitored by a UN force since 1974 in the wake of the Arab-Israeli War.
Syrian rebels and their relatives began evacuating the southern city of Daraa on Sunday, an AFP correspondent and a monitor said, more than seven years after the country's ill-fated uprising erupted there.
Furthermore, the ground troops succeeded in gaining Al-Taiha northern countryside of Daraa province and Tal Mashara, Mashara town which stationed in the countryside of Quneitra province.
Under some of these deals, Russian military police would oversee local security - rather than Syrian government forces - and rebels would become part of Russia-supervised local security forces.
Deraa city was the scene of the first major peaceful protests against Syrian President Bashar al-Assad's authoritarian rule in March 2011.
Iran and Israel were heading towards a direct confrontation in one of the most keenly contested territories in the Middle East, as forces loyal to the Assad regime and Tehran routed rebels in Syria.
On Sunday, government forces fired hundreds of missiles in the first such attack on the province in more than year when Russian Federation, the United States, and Jordan agreed to a ceasefire for parts of the south, the Syrian Observatory for Human Rights said. On Sunday, the first batch of armed fighters and their families were preparing to leave from the city of Daraa, the provincial capital, in buses that would take them to the rebel-held Idlib province in the north.
The so-called "reconciliation" deal for Daraa city is the latest in a string of such agreements the regime has used to retake large parts of the country.
Brewers’ Aguilar falls short in Home Run Derby
Bryce Harper , who said he was exhausted after taking his cuts in the first round, certainly appeared gassed in the final round. Who's in the Derby this year? Against Kyle Schwarber he rallied hard, matching Schwarber's 18 home runs in the last second.
"Syrian ... forces captured the town of al-Harah, as well as Samlin, al-Tiha and Zimrin", media outlets quoted observatory chief Rami Abdel Rahman as saying.
They usually follow ferocious military campaigns and sometimes stifling sieges that effectively force rebels to surrender.
The regime fully regaining its rule over Daraa city will be a hugely symbolic blow to the opposition.
Assad has regained much of the territory he initially lost to opposition groups, now comfortably holding more than 60 percent of Syria.
Syrians ride a vehicle carrying their personal belongings as they return to their homes in towns and villages situated on the eastern outskirts of Daraa on July 7, 2018.
Quneitra province borders the Israeli-occupied Golan Heights. The Observatory said government forces advanced on Massharah, a village in Quneitra, and rebels fought back in intense clashes that killed several pro-government fighters.
"The Syrian jets do not dare to reach the Quneitra area due to an agreement struck between Russian Federation and Israel in the southern front", Qahwaji said.
Israel has been on high alert in recent weeks amid the spike in hostilities in the south.
- Photos of the christening of Prince Louis - cute! - CBBC Newsround
- Nathan Fillion Is Nathan Drake In Incredible 'Uncharted' Fan Film
- Ozil to travel with Arsenal to Singapore
- Trump's Supreme Court Nominee Donated Money To Ohio Democrat
- LeBron thrills fans by showing up to summer league in Lakers shorts
- Uber update turns iPhone into a colorful light to flag your driver
- Google updates phone app to prevent some spam calls from interrupting you
- Showtime defends Sacha Baron Cohen against Sarah Palin
- Negligence Kills Eight Black Rhinos in Kenya
- Villagers kill hundreds of crocodiles after death of local man