Syrians began fleeing an area east of Aleppo city on Thursday after the army gave civilians a deadline to leave amid fears of an escalation in clashes with Kurdish forces.
The government is seeking to extend its authority across the country following the ouster of longtime leader Bashar al-Assad a year ago.
On Sunday, government troops took full control of Aleppo city over the weekend after capturing two Kurdish-majority neighbourhoods.
It reached a deal in March to fold a Kurdish de facto autonomous administration in the north into the state, but progress on its implementation has stalled.
An AFP correspondent near Deir Hafer, one of the Kurdish-controlled towns being eyed by Damascus, saw many cars, trucks and civilians on foot leaving through a corridor set up by the army on Thursday, but the road was due to close at 5:00 pm (1400 GMT).
Mahmud al-Mussa, 30, said "thousands of people have not left", accusing the US-backed, Kurdish-led Syrian Democratic Forces of not letting them leave.
"They want to use civilians as human shields," he said.
The area targeted extends from near Deir Hafer, around 50 kilometres (30 miles) from Aleppo, to the Euphrates River about 30 kilometres further east, as well as towards the south.
Damascus, which has deployed forces to the region, also accused Kurdish forces of barring the civilians from leaving.
Farhad Shami, spokesperson for the SDF, told AFP the accusations were "unfounded".
Nadima al-Wayss, 54, said she, her brother and her niece had to cross a damaged bridge to leave Deir Hafer through a different road.
"Good people helped me cross the bridge... I was afraid I would fall."
- 'Join hands' -
The SDF controls swathes of Syria's oil-rich north and northeast, much of which it captured during the country's civil war and the fight against the Islamic State group over the past decade.
In a statement on Thursday, the Kurdish-led autonomous administration said they remained open to dialogue with Damascus and called on the international community to prevent a new civil war in Syria.
The SDF warned that the escalation "could lead to general instability, posing a real threat to the security of prisons holding ISIS members", referring to the Islamic State (IS) group.
Camps and prisons in Syria's Kurdish-administered northeast hold tens of thousands of people, many with alleged or perceived links to IS, more than six years after the group's territorial defeat in the country.
Syrian President Ahmed al-Sharaa said "the ball is in (the SDF's) court", calling on the group to "join hands with us... and begin the reconstruction process in Syria".Â
He made his remarks in an interview with Iraqi Kurdish channel Al Shams, which then decided not to air it.
Syrian state television and other regional channels have since aired excerpts.
"The agreement signed by Mazlum Abdi does not include federalism, self-administration... it includes a unified Syria," Sharaa said, referring to the SDF leader.
The Kurds have called for a decentralised federal system as part of their integration process into the Syrian state, but Sharaa has rejected their demands.
Syria's Kurds faced decades of oppression under former president Assad and his father, Hafez, who preached a Baathist brand of Arab nationalism.
They fear Syria's new Islamist rulers may take away from them the autonomy they carved out during the civil war that erupted with Assad's 2011 crackdown on nationwide democracy protests.
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