The Syrian regime gave on Sunday rebels in the Hrasta pocket in the rebel-held Eastern Ghouta enclave until 3 p.m. to leave the area.
In a month-long assault, pro-Syrian regime forces have marched into much of Eastern Ghouta, the last major insurgent bastion around Damascus.
They have splintered it into three besieged zones, the smallest of which is the Harasta pocket.
Earlier, the main rebel group in the southern pocket of Eastern Ghouta told Reuters it was negotiating with a United Nations delegation about a ceasefire, aid and the evacuation of urgent medical cases.
"We are engaged in arranging serious negotiations to guarantee the safety and protection of civilians," said Wael Alwan, the Istanbul-based spokesman for Faylaq al-Rahman, in a voice recording.
"The most important points under negotiation are a ceasefire, ensuring aid for civilians and the exit of medical cases and injured people needing treatment outside Ghouta."
Alwan said the subject of "exit and evacuation" was "not on the table".
A number of patients requiring urgent medical attention have been evacuated from the northern pocket and some aid has entered there.
This has not yet happened in the southern pocket.
The UN office for the coordination of humanitarian affairs (OCHA) said in a statement on Thursday at least 20,000 people have left Eastern Ghouta in the past week, the majority of which came from the southern pocket through the Hammouriyeh area.
The regime opened a corridor near Hammouriyeh this week and civilians have been making their way out towards army positions on foot, hauling their belongings with them.
OCHA said conditions for those remaining in eastern Ghouta are "dire".
"There is limited food, with reports of the usual ration of bread for one day being consumed over the period of a week to 10 days; insufficient sanitation and hygiene support for those living in basements, and increased risk of communicable disease," it said.
On Saturday, the Syrian Observatory for Human Rights said 30 people were killed in a Saturday morning airstrike on Zamalka that hit a group of people trying to flee into regime-controlled areas.
The opposition's Syrian Civil Defense said the airstrike killed dozens and wounded scores, adding that paramedics are trying to help survivors.
"The world has betrayed us," said Ahmad Khanshour, a resident of Eastern Ghouta, referring to the international community that could not do much to stop the offensive. "The world betrayed itself and the human values we all once shared."
Syrian regime forces launched the major offensive in Eastern Ghouta on February 18 and now control over 80 percent of the regions. Tens of thousands of civilians have fled in recent days.
More than 20,000 people have left Eastern Ghouta via Hammouriyeh so far on Sunday, the Interfax news agency reported, citing the Center for Reconciliation in Syria, a body run by Russia's Defense Ministry.
Since humanitarian corridors were set up in the area, more than 68,000 people have left the enclave, the center said.
