By Suleiman Al-Khalidi

BEIRUT (Reuters) - The Syrian army and the Lebanese Hezbollah militia said they had launched a major ground and air assault on the rebel-held Syrian city of Zabadani on Saturday and were closing in on insurgents holed up inside.

The army, with its Shi'ite ally Hezbollah, has long sought to wrest control of Zabadani from Sunni rebels who have held it since 2012, a year after the start of the Syrian civil war. The city is near the Lebanese border and the Beirut-Damascus highway that links the countries, and so capturing it would be a major strategic gain for Syrian President Bashar al Assad's government.

Footage released on Hezbollah's TV channel al Manar and Syrian state TV showed large plumes of smoke rising from the city, and the sounds of aerial bombardment and heavy artillery shelling could be heard. New footage showed artillery rounds being fired from high ground in a mountain range that surrounds the Zabadani towards the center of the city.

The once popular resort city, northwest of the capital Damascus, is one of the rebels' last strongholds along the border. It was part of a major supply route for weapons sent by Syria to Hezbollah before the 2011 outbreak of the Syrian conflict, which has killed over 200,000 people.

The Syrian army said it had inflicted heavy casualties on "the terrorist groups fortified inside the city" and was advancing from several fronts towards their positions.

A hilltop west of Zabadani that overlooks rebel positions, known as Qalat al Tel, was also captured, the army said.

The rebels said they had planted mines around the city, which is now mostly deserted, and were well prepared to repel the assault.

The assault began at dawn with a heavy barrage of missiles accompanied by dozens of aerial bombings raids and a large deployment of ground troops, rebel sources said.

The insurgents, using ex-Russian army tanks and long-range artillery, pounded army positions and prevented any advance, said Abu Ado from the Islamist Ahrar al-Sham brigade.

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"The bombardment is not stopping from the air, from helicopters, and missiles fired from artillery vehicles, and they are trying to advance, but God is with us," the rebel commander told Reuters from the battlefield.

The Syrian military and pro-government fighters have regularly clashed with insurgents in the mountainous area north of the capital, and violence from the four-year-old civil war has regularly spilled over into Lebanon. The rebel groups in the area include al Qaeda's Syrian wing, the Nusra Front.

Iranian-backed Hezbollah - which has been a crucial ally to Assad, sending fighters to bolster his forces - has in recent months stepped up its assault on rebel outposts along the Qalamoun mountain region straddling the Lebanese Syrian border.

The aim of the campaign was to cut rebel arms supply routes along the rugged border terrain.

A major military campaign by the Syrian army and the Lebanese group to capture Zabadani, which is part of Assad's effort to shore up his control over western Syria, had been expected in recent days.

The Syrian army is fighting on several other fronts; as well as battling rebels around the southern city of Deraa and the northern city of Aleppo, it has been fighting Islamic State as the militant group attempts to seize government-held areas of the northeastern city of Hasaka.

(Editing by Pravin Char and David Evans)