BEIRUT: The Syrian army backed by Lebanese ally Hezbollah has advanced deeper into the besieged Syrian city of Zabadani two weeks into a campaign to capture it from insurgents, rebels and the army said.

The control of the city, about 45 km (30 miles) northwest of the capital Damascus, is seen as crucial to consolidate government-held areas linking Lebanon and Syria. Zabadani is a former popular resort on the main Beirut-Damascus highway.

Hezbollah militiamen and the army, aided by reinforcements, advanced closer to Zabadani's centre under cover of heavy artillery fire and intense aerial bombardments of insurgent hideouts, rebels and the army said.

Footage released by the Syrian army showed troops in the heart of the southeastern district of Sultani, the focus of street fighting. Rebels said some 500 families were still inside Zabadani and had taken shelter but the city was mostly deserted.

Its capture would be a strategic gain for Syrian President Bashar al-Assad, whose army is battling on several other fronts with groups including non-jihadist rebels and hardline Islamic State militants.

A victory over the rebels would also secure a corridor for Hezbollah to transport fighters and arms. The Shi'ite Muslim group's military role inside Syria has been growing steadily since the start of the conflict in 2011.

Rebels contacted by phone said although they had lost some ground in parts of the city in the last few days, they have so far repulsed advances deeper inside their stronghold.

"They have now secured what they want...any more advances would be very costly in human terms for them," said Abu Abdo, a field commander from the Ahrar al-Sham insurgent group.

Around 1,500 to 2,000 fighters from Islamist groups including Ahrar al-Sham and al-Qaeda's Syrian offshoot Nusra Front alongside local fighters have dug inside the city that was besieged by the army even before the last assault.

The army cut an insurgent supply route from neighbouring rebel held town of Madaya to Zabadani two days ago, part of a move to further tighten the seige around the city and to sever supplies to insurgents from outlying areas.

The Sunni Muslim rebels in Zabadani have appealed to their counterparts in the Ghouta suburbs of Damascus further southeast to escalate attacks to relieve pressure on them.

The area around Zabadani was part of a supply route for weapons sent by Syria to Hezbollah before the outbreak of the Syrian conflict, which has killed more than 200,000 people.

The army and Hezbollah captured the western mountains overlooking Zabadani last March but rebels who control the eastern hilltops have used rocket launchers to hit their positions.