A Russian-brokered deal had been reported on Sunday for fighters with Jaish al-Islam, the largest rebel group still in Ghouta, to leave the enclave's main town of Douma.
But the rebels have not yet confirmed the agreement, amid reports of divisions in the group as hard-line fighters refuse to abandon their posts.
The retaking of Eastern Ghouta would mark a major milestone in President Bashar al-Assad's efforts to regain control of territory seized by rebel factions during Syria's seven-year civil war.
Assad's forces have retaken 95 per cent of Eastern Ghouta since launching a blistering assault on the besieged enclave on February 18, killing 1,600 civilians and displacing tens of thousands more.
State media on Monday said Jaish al-Islam fighters and members of their families had started leaving Douma in preparation for them heading to a rebel-held town in northern Syria.
Civilians stay put despite 'pause' in Syria Ghouta bloodshed
Buses carrying 1,146 Jaish al-Islam members and their families left Douma headed for Jarabulus, after a wait of several hours, state news agency SANA said.
Pro-regime newspaper Al-Watan said in an editorial on Monday it was a matter of hours until Douma was declared a "town empty of terrorism".
"The town of Douma has come closer to joining other villages and areas of (Eastern) Ghouta taken back by the army," it said.
The rebels have been negotiating with Russia, a key ally of Assad, for days on an agreement to evacuate Douma.
Late on Sunday, Russian news agency Interfax quoted General Yuri Yevtushenko as saying a "preliminary deal" had been reached to evacuate Jaish al-Islam fighters.
The Syrian Observatory for Human Rights monitoring group on Monday reported divisions within the ranks of Jaish al-Islam, which has previously said it would not leave Douma.
"There are attempts to convince the hardline wing of Jaish al-Islam not to obstruct the agreement with the Russians," said the head of the Britain-based monitor, Rami Abdel Rahman.
In video footage published by Jaish al-Islam online on Sunday, the group's leader told a group of men in a mosque he would stay put.
"We will stay in this town and will not leave. Those who want to leave should leave," Essam al-Buidani says in the video, although it was unclear when it was filmed.
Jaish al-Islam counts around 10,000 fighters, according to the Observatory.
Elderly Pakistani couple leave Syria's embattled Ghouta, says Red Crescent
Backed by Russia, Assad's forces have scored a series of victories over rebel forces in recent years, often through campaigns of siege, aerial bombardment and ground offensives that have drawn widespread international condemnation.
Before February 18, some 400,000 people in Eastern Ghouta had lived under regime siege for five years, facing severe food and medicine shortages.
After pounding it with air strikes, regime forces have taken back most of the enclave through a combination of ground assaults and Russia-brokered evacuation deals.
In the past few weeks, these deals have seen more than 46,000 people — fighters and civilians — board buses with scant belongings to be driven to the north western province of Idlib, which is largely outside government control.
These include more than 1,000 people — fighters from another faction, Faylaq al-Rahman, and family members — who left Douma late Sunday, according to state media.
On Monday before dawn, an AFP correspondent saw men, women and children step off buses in the area of Qalaat al-Madiq in central Hama province, a way station on the road to Idlib.
An old woman dressed head-to-toe in black stood by a pile of suitcases, with a child wearing a winter coat and colourful backpack by her side.
A man had a gun slung on his shoulder as he picked up a travel bag, while a young boy, who appeared weak and unable to move his limbs, was carried into an ambulance.
A man in a long white robe walked on crutches, a light weapon visible under his khaki jacket.
Syria's war has killed more than 350,000 people and displaced millions since starting in 2011 with a brutal repression of anti-regime protests.
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