The clashes on Wednesday - which involved Russian air strikes on Western-backed rebel groups - came as the Syrian government attempts to capture Sheikh Maskin, an area crucial to its attempts at gaining control of southern Deraa province.
The Syrian offensive was the first by the government in southern Syria since Russian forces entered the war in support of President Bashar al-Assad in September.
"The army is making progress with heavy Russian aerial bombing. The raids are not stopping. We have had over 40 raids in the last 24 hours alone," rebel commander Abu Alaa al-Haurani told the Reuters news agency.
Haurani is a member of al-Failaq al-Awal, part of the Southern Front alliance of 54 rebel groups fighting as part of the Free Syrian Army.
Syria's army said that it had made advances overnight against the rebels it said were mainly al-Qaeda-inspired groups.
Sheikh Maskin, the main goal of the army's southern campaign, lies on one of the main supply routes from the capital Damascus to the city of Deraa, close to the border with Jordan.
The UK-based activist group Syrian Observatory for Human Rights said clashes were ongoing and there had been losses on both sides.
Moscow claims it mainly targets the Islamic State of Iraq and the Levant (ISIL) group, but the US and other Western powers have accused it of a broader campaign aimed at rebels fighting government forces.
Earlier this week, a suspected Russian air strike killed Syrian rebel leader Zahran Alloush and several of his commanders in the Damascus suburb of Ghouta.
Alloush had been involved in fighting against both the Syrian government and ISIL.
Syria's civil war will mark its fifth anniversary in March. The conflict began when an initially peaceful revolt against Assad was put down with deadly force.
The first protests against Assad's rule started in Deraa province and quickly spread to other parts of the country.