* Evacuees destined for rebel-held northern areas
* Trucks piled high with belongings
* Offensive restores state control over southwest swathe (Adds Reuters witness account)
By Ellen Francis and Rami Amichay
BEIRUT/GOLAN HEIGHTS, July 20 (Reuters) - Syrian rebels began evacuating the border with the Israeli-occupied Golan Heights on Friday, leaving for the rebel-held north in a surrender deal that restores President Bashar al-Assad's control of the frontier.
With a Russian-backed government offensive closing in, rebels in Quneitra province have agreed to either accept the return of state rule, or leave to Idlib province in the north in another major victory for Assad.
Buses transporting both rebels and civilians fearing government persecution began leaving the Quneitra area in the mid-afternoon, a witness said.
A military news service run by Lebanon's Hezbollah, which is fighting in support of Damascus, said buses "carrying militants" had left the city of al-Quneitra headed north.
A Reuters witness at a vantage point on the Israeli-occupied Golan Heights saw a steady movement of people out of the village of al-Qahtaniya, near Quneitra. A stream of motorcycles, heavily laden cars and flatbed trucks packed with men, women and children departed the village.
The offensive has restored Syrian government control over a swathe of the southwest. It has been one of the swiftest campaigns of the seven-year-long war. The United States, which once armed the southern rebels, told them not to expect its intervention as the attack began. Many surrendered quickly.
While swathes of Syria remain outside his control, Assad's advances over the past two years have brought him ever closer to snuffing out the armed rebellion that grew out of a civilian uprising against his rule in 2011.
It leaves the insurgency with one last big foothold - a chunk of territory in the northwest at the border with Turkey stretching from Idlib province to the city of Jarablus northeast of Aleppo. The deployment of the Turkish military in that area may complicate the next phase of the war for Assad.
Idlib's population has been swollen by Syrians fleeing from Assad's advances elsewhere.
Large areas of the northeast and east also remain outside Assad's grasp. These areas are held by Kurdish-led militias, supported by 2,000 U.S. troops on the ground.
MOVING MATTRESSES, BAGS AND BUNDLES
The Hezbollah-run military news service said Syrian government forces had taken control of several villages in Quneitra province.
The people leaving Qahtaniya were heading in the direction of Quneitra, though their eventual destination was unclear.
The Reuters witness saw dozens of large passenger buses arriving in the village, lined up on the side of the road. They sped off after two or three hours. Most headed south, but some went in an easterly direction.
The movement was steady rather than panicked, but was punctuated by occasional bursts of gunfire. Some, but not many, of the men were armed and some were wearing masks and flak jackets.
They could be seen moving mattresses, bags and bundles out of buildings, while others carried larger metal objects. One group pushed motorcycles off the road and set fire to them, while smoke also rose from behind a cluster of buildings.
A small number of military-style vehicles were visible in the streets - including one pickup truck with a heavy rear-mounted gun, but there was no sign of clashes in the village streets. By mid-afternoon the village was much emptier but it was not clear if everybody had left.
Late afternoon, around 3.30pm local time, the Reuters witness saw several buses leaving Quneitra, northwest of al-Qahtaniya.
The U.N. refugee agency UNHCR appealed to all sides in Syria to provide safe passage for 140,000 civilians displaced by fighting in the southwest so that they can receive aid and shelter.
The offensive triggered the biggest single displacement of the war, with 320,000 people uprooted at first. UNHCR said tens of thousands of displaced people had returned following local agreements in areas that returned to state control. (Additional reporting by Kinda Makieh in Damascus and Stephen Farrell in Jerusalem; writing by Tom Perry and Stephen Farrell; editing by Alison Williams, Angus MacSwan, William Maclean)
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