The attack hit the village of Hader, populated by members of the Druze majority, which lies near the disengagement line that divides the Syrian-controlled part of the Golan from that occupied by Israel.
The fighting prompted concern from Druze residents of the Israeli-occupied Golan Heights, and a statement from the Israeli army, which pledged to "prevent Hader from being harmed or occupied".
The assault began when a suicide car bomb attacked the outskirts of the village, Syrian state media said.
Al-Nusra Front is the old name for a jihadist group that was formerly Al-Qaeda's affiliate in Syria and is now known as the Fateh al-Sham Front.
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"In the aftermath of the terrorist attack, terrorist groups carried out a heavy attack on Hader, and army units and the Popular Defence units (pro-government militants) clashed with the attackers," SANA added.
The agency said the toll was expected to rise because a number of those wounded in the bombing were in serious condition and the ongoing assault on the town made it difficult to remove the injured to safety.
The Syrian Observatory for Human Rights, a Britain-based monitor, said the clashes that followed the blast killed several forces on both sides.
Hader lies in southwestern Syria's Quneitra province, around 70 per cent of which is held by either rebel or jihadist groups while the government controls the remaining 30 per cent, according to the Observatiory.
Some Syrian Druze have expressed sympathy for opposition forces battling the government since the start of the civil war but the community has largely been loyal to the regime.
Israel seized 1,200 square kilometres (460 square miles) of the Golan Heights from Syria in the Six-Day War of 1967 and later annexed it, a move never recognised by the international community.
But it has bombed Syrian territory on a sporadic basis, sometimes in response to stray Syrian army fire.
On other occasions, it has been accused of carrying out air strikes targeting weapons intended for Hezbollah, the Lebanese militant group that is an ally of Damascus but has fought Israel.
The Israeli army said today that a civilian in the town of Majdal Shams in the Israeli-occupied part of the Golan was lightly wounded as a result of "shots fired from Syria".
Israeli army spokesman, Brigadier General Ronen Manelis, said the military was ready to "prevent Hader from being harmed or occupied, as part of our commitment to the Druze population".
Nearly 140,000 members of the Druze minority, which follows a secretive offshoot of Shiite Islam, live in Israel and the Israeli-occupied Golan.
In Majdal Shams, Druze residents gathered along the buffer zone seeking to cross over and help.
Around 10 of them entered the buffer zone, the Israeli army said, before forces caught them and returned them to the Israeli-occupied side.
Speaking from London, Israeli Prime Minister Benjamin Netanyahu said "we safeguard our borders. Our borders in the south, our borders in the north. And we also cherish our sympathy for our Druze brethren".
Israel has a policy of providing medical assistance to Syrians wounded in the conflict, transporting some into its territory for treatment.
The policy has been controversial, and in 2015, members of the country's Druze minority attacked two ambulances transporting Syrians, killing one and injuring another.