A Syrian rebel commander in the south vowed to wage guerrilla war against the Lebanese group Hezbollah and Syrian government forces which have launched a major offensive against insurgents in the sensitive border region near Israel and Jordan.

The offensive that got under way this week is focused in an area south of Damascus that is the last notable foothold of the mainstream armed opposition to President Bashar al-Assad, who has consolidated control over much of western Syria.

The Syrian Observatory for Human Rights, which tracks the war, says the push is being spearheaded by Hezbollah, and that government forces and allied militia have made significant progress.

The Syrian army said on Wednesday that territory including four hills and three towns had been secured from insurgents it identified as members of the al Qaeda-linked Nusra Front.

The mainstream rebels known collectively as the Southern Front are dismissive of Nusra's role in the area. The battle -- the most serious effort to date by the state to take back the south -- was mostly brought to a halt on Thursday by snow.

"The battle could be lengthy. It will be hit and run -- this is the system we are going to use in battle," said Abu Osama al-Jolani, a senior commander in the southern rebel alliance.

"We are not a state army defending borders ... we operate a system of guerrilla warfare. As far as we are concerned, land is not important," he added, speaking to Reuters via the Internet from an area near the Syrian-Jordanian border.

Jolani, who held the rank of major when he defected from the Syrian army in 2011, said the attacking forces had sustained heavy losses and their gains were insignificant. He is now deputy commander of the "First Army", formed from three smaller rebel groups in January.

Rami Abdulrahman, who runs the Observatory, said four days of fighting had killed 19 combatants on the government side and 48 on the opposition side. He said the advances by Hezbollah and the government should not be underestimated.

Hundreds of Hezbollah Fighters

The Syrian defence minister visited the frontline on Thursday, Hezbollah's al-Manar TV station reported.

The Southern Front rebel alliance includes groups that have received support from foreign states opposed to Assad. The support has included what the rebels describe as small amounts of military aid, including some U.S.-made anti-tank missiles.

With much of the north and east held by jihadist groups including the powerful Islamic State, the southern rebels see themselves as the last bastion of the revolt against Assad that erupted in 2011 before descending into civil war.

The opposition complains that while the Syrian government has received vital military support from Assad's allies, including Hezbollah and Iran, Arab and Western states that want to see Assad gone have failed to do the same.

A Lebanese columnist close to Hezbollah wrote on Wednesday that the decision to launch the southern offensive had been taken several weeks ago at the highest levels of the "Resistance Axis" - a reference to Syria, Iran and Hezbollah.

The battle is being waged a short distance from the Israeli frontier on the Golan Heights, a sensitive area at the intersection of Syria, Lebanon and Israel.

An Israeli official briefed on intelligence said the current offensive "involves Hezbollah more heavily than in previous operations". "There are hundreds of their fighters involved," said the official, speaking on condition of anonymity.

Jolani said the Syrian army was playing no role in the battle. "This is a very important test for the Southern Front," he said. "We ask all the states of the world to help the Syrian people and to help us the way Iran and Russia help the regime."