Southwestern Syria is one of two remaining rebel strongholds, along with a region of the northwest that Syrian President Bashar al-Assad has sworn to recapture.
After retaking control of eight towns under Russia-mediated deals on Saturday, Assad's regime now controls more than half of Daraa province, up from just 30 percent before the escalation, according to the Observatory.
"Thousands are already reported to have fled their homes but there is also the grave risk that the intensified fighting will see many civilians trapped, caught between Syrian Government forces and their allies on the one hand and armed opposition groups and ISIL on the other", said Zeid.
The strategic southwestern corner of Syria had been under a so-called de-escalation agreement reached between Russian Federation, the United States and Jordan in July of previous year, but the truce has unraveled in recent weeks. State TV broadcast scenes of what they said were locals celebrating the army's arrival in the formerly rebel-held town of Ibta and said rebels turned in their weapons.
The government's offensive so far has focused on Deraa province, which borders Jordan, but not Quneitra province abutting the Israeli-occupied Golan Heights. Jordan, which is already hosting 660,000 registered refugees, says it can not accept any more and has sealed its border, despite appeals from aid groups. Another rebel official said some towns were trying to negotiate deals with the state on their own.
A video released by Israel's military shows soldiers loading aid into trucks on the Israeli-controlled side and the cargo being then carried into vehicles by unidentified people on the Syrian side of the border.More news: Verstappen used secret tactic to win Austrian Grand Prix
Jordan has been facilitating talks between rebel factions and Moscow over a deal that would end the violence in exchange for the return of state rule in Deraa province on its border.
Talks failed on Saturday after a meeting in which Russian officers met the rebel team and demanded a complete surrender, rebels said.
Since June 19, Russian-backed government forces have been battering opposition-held parts of Daraa Province with airstrikes and barrel bombs, simultaneously calling on rebels to surrender.
The civilian delegation abandoned the negotiations "in light of the lack of clarity in the discussions and the Russians' insistence on imposing their conditions", the statement, authored by delegation leader Adnan Musalma, read.
Local websites reporting news about Ramtha claimed that dozens of mortar shells have lost their way into their area since the beginning of the attack on Daraa nearly two weeks ago.
Almost 100 civilians have been killed since the assault began on June 19 with airstrikes, rocket fire and crude barrel bombs.