Beirut, Lebanon (CNN) Thousands of people continued to flee from battlegrounds in northern and southern Syria on Friday amid reports that rebels in a Damascus suburb were preventing some residents from leaving the besieged area.

At least 10,000 people flooded out of the town of Hamoriya in Eastern Ghouta on the outskirts of the capital Thursday, one of the largest single-day exoduses of the war, which has now entered its eighth year.

The Syrian ambassador to the United Nations claimed Friday the number could be as high as 40,000, but CNN cannot confirm that figure. Hundreds of people continued to leave the area Friday, according to the United Nations.

Eastern Ghouta, a suburb on the edge of the capital, is one of the last major rebel-held areas in Syria. A brutal military onslaught there has left more than 1,000 dead since mid-February.

Meanwhile, 48,000 people have fled a Turkish assault in the Kurdish-held enclave of Afrin, in northwest Syria, in the past few days, the United Nations told CNN.

Turkey, a NATO ally, launched an operation in January targeting Kurdish groups -- some of them backed by the United States -- in Afrin province to clear the border area of militias it considers to be terrorist organizations.

UN Secretary-General Antonio Guterres said in a statement Friday that he was "deeply concerned by the desperation shown by the people fleeing in a massive exodus from Eastern Ghouta and Afrin."

Ghouta rebels 'keeping some civilians from leaving'

Images on Syrian state TV showed hundreds of people carrying their belongings out of Eastern Ghouta on foot and in the back of pickup trucks Thursday. Soldiers were seen in the footage, but there were no signs of local or international aid groups. The Red Cross told CNN it was not involved in the exodus.

But some residents in Douma, the largest town in Eastern Ghouta, were barred from leaving by rebels despite begging international aid groups for help, an official who was on the ground in Douma on Thursday told CNN.

"What I can tell you also from (Thursday) is many people want to go out," said the official, who spoke to CNN on the condition of anonymity.

Syrian civilians, evacuated from rebel-held areas in Eastern Ghouta, gather at a school on the northeastern outskirts of the capital Damascus on March 16, 2018.

The source witnessed firsthand an encounter between a woman slated to be medically evacuated with her family, members of the Syrian Arab Red Crescent tasked with escorting the family out of Douma, and rebel fighters.

Members of the rebel group ordered the woman's 16-year-old son to stay behind.

"I saw the discussion between the group inside and SARC (the Syrian Arab Red Crescent) and the woman who was begging to get her little son out of the area. They didn't accept that," the official said.

"She was completely desperate and she wanted to take her son out, but they didn't let her go, and SARC couldn't do anything about it. ... They have to get approval of the groups who are inside," the official added.

The entire family, which included a blind girl and an ill older man, were to be escorted by SARC out of the enclave. SARC medical evacuations are meant to include not only the sick and wounded, but also their immediate family members.

SARC did not immediately respond to CNN's request for comment.

Syrian civilians evacuated from Eastern Ghouta wait to be relocated to other areas.

Russia, one of Syria's key allies, ordered the opening of a humanitarian corridor in Douma last month to allow civilians to leave rebel-held parts of Eastern Ghouta. But the official who spoke to CNN says no one would "dare to leave" through that corridor -- which is separate from the route thousands took out of Hamoriya Thursday -- without a humanitarian escort.

The Syrian regime and rebel fighters have accused each other of shelling the roughly 5-kilometer-long passage leading from Eastern Ghouta to relative safety in government-held areas of the capital.

Given the dangers of using the corridor without an escort, the only hope for residents is to be put on a medical evacuation list -- which already has more than 1,000 names -- and to be accompanied out by the Syrian Arab Red Crescent, the source and an analyst said.

Syrian civilians evacuated from rebel-held areas in the Eastern Ghouta enclave gather at the school in the regime-controlled Adra district.

"Some of the armed groups do actively prevent people leaving from Eastern Ghouta," Chris Doyle, director of the Council for Arab-British Understanding, told CNN.

"The fighters who are obviously holed up in a corner are using all means at their disposal, including preventing civilians from leaving them to defend their position. You could argue that it's a form of human shields."

Doyle, who said he regularly speaks to residents in Eastern Ghouta, said rebel groups and government forces were both to blame for the suffering of the people there.

"The civilians in Ghouta are very much trapped between two sides," Doyle said.

Eastern Ghouta has been under siege since 2012, but the Syrian military has advanced steadily through the area over the past month, starting with villages and towns in the east before splitting the rebel-held areas of the suburb into three parts last week.

The offensive has been carried out with the support of Russia and in defiance of a United Nations call for a ceasefire.

Observers say it is now only a matter of time before the regime takes control of the entire enclave.

Civilians flee the city of Afrin in northern Syria on March 16, 2018.

'Worrying' situation in Afrin

A total of 48,000 people have been displaced from the Afrin region in the past few days, Russell Geekie, a spokesman for the United Nations Office for the Coordination of Humanitarian Affairs, told CNN on Friday.

Around 35,000 left from the city of Afrin and a further 13,000 from surrounding areas, Geekie said.

According to Turkey's state-run Anadolu agency, Turkish forces said Tuesday they had encircled the city of Afrin.

In a briefing to the UN Security Council on Friday, Staffan de Mistura, UN special envoy for Syria, described the situation in Afrin as "particularly worrying," citing reports of tens of thousands of people displaced and civilian casualties.

He urged all parties "to ensure that those civilians seeking to leave Afrin be given safe passage."