Syrian troops and members of Lebanon's Hezbollah have advanced against Syrian rebels on the second day of an assault to drive them from their last foothold along the Syria-Lebanon border, pro-Damascus media reported.

The government-controlled Syrian Central Military Media (SCMM) said Shia Hezbollah fighters and Syrian troops captured several strategic hills on Saturday in areas between the Lebanese town of Arsal and the Syrian village of Fleeta.

The offensive began on Friday and targets Sunni Muslim fighters from the former al-Nusra Front, a group that was aligned to al-Qaeda.

It is now known as Hay'et Tahrir al-Sham and controls the barren zone of Juroud Arsal in the Qalamoun Mountains.

READ MORE: Syria's civil war explained from the beginning

SCMM said Syrian warplanes struck rebel positions on the Syrian side of the border on Saturday.

A military unit run by Hezbollah said its forces captured a strategic hilltop area called Dhahr al-Huwa, previously a key al-Nusra Front base, and other areas in southern Juroud Arsal.

Hezbollah, backed by Iran, has fought alongside Syrian President Bashar al-Assad's forces in Syria's civil war since 2013.

Lebanon's National News Agency reported that the former deputy mayor of Arsal, Ahmad Fliti, was killed when a rocket fired by rebel fighters hit his car.

He was killed while on a mediation mission with Hay'et Tahrir al-Sham.

A security source put Hezbollah's death toll at 15 early on Saturday, and told Reuters news agency that at least 43 Syrian rebels had been killed.

Footage on Hezbollah's Al Manar TV channel showed fighters on a hilltop firing assault rifles and wire-guided missiles at rebel positions.

Some rebel fighters had raised white flags in surrender, it reported.

The Lebanese army, which is not taking part in the offensive, has taken up defensive positions around Arsal town, ready to fire at Sunni fighters trying to break through its lines.

It was also facilitating the passage of Syrian refugees fleeing the area, with UN supervision, a security source told Reuters.

Several thousand Syrian refugees occupy camps east of Arsal, a mainly Sunni town.

In 2014, it was the scene of one of the most serious spillovers of the Syrian war into Lebanon when fighters briefly overran the town.