(CNN) - Airstrikes rained down again Saturday in the Syrian enclave of Eastern Ghouta, according to activist group Damascus Media Center, as swarms of civilians continued to pour out of the battered rebel-held area not far from the nation's capital.
Officials with different groups have placed widely varying figures of the number of refugees who are leaving Eastern Ghouta. The UN Office for the Coordination of Humanitarian Affairs (OCHA) says more 12,000 people have fled in the past few days. Syria's ambassador to the United Nations says it is more than 40,000.
CNN cannot independently confirm the exact number of people fleeing as the advancing Syrian military continues to pound rebel targets in the eight-year civil war.
Images show what appear to be hundreds of civilians -- many with children in their arms -- walking to a safe passage corridor as they exit the territory. The Syrian Arab Red Crescent is securing those fleeing and moving them to temporary living centers, according to Syrian state television. The Red Crescent sent CNN photos of people it had helped.
The World Food Program in Syria has been receiving refugees in three shelter centers in the Damascus area.
Eastern Ghouta has been under siege since 2012, but the Syrian military has moved forward 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.
Staffan de Mistura, the UN special envoy for Syria, on Friday called the situation dire for those fleeing and the several hundred thousand people who remain.
"Even for experienced people like my own humanitarian colleagues, it was an unsustainable situation where people are literally at the tip of a collapse," he said.
De Mistura urged fighters on both sides to let the refugees have safe passage.
But it appears that is not happening for some who want to leave.
In Douma, the largest town in Eastern Ghouta, rebels barred some from leaving despite residents 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.
Well to the north, near Syria's border with Turkey, tens of thousands of people were also fleeing the fighting, in this case involving the Turkish military.
Turkish troops move into northern Afrin
Two groups of Turkish troops fighting militia members met in northern Afrin on Saturday, according to Turkey's state-run news agency Anadolu.
President Recep Tayyip Erdogan said Turkey lost many troops but said many "terrorists" also were killed or captured.
"We said patient people would reach to the victory and we did," he said.
Turkey, a NATO member, launched "Operation Olive Branch" on January 20, targeting Kurdish groups -- some of them backed by the United States -- to clear Afrin province of militias it considers to be terrorist organizations.
The fighting has been fierce at times.
The general manger at a major hospital in Afrin told CNN nine people were killed when the facility was bombed this week.
Only a small section of the complex is operational.
"The situation is really bad. There are reports of dozens of bodies on the road out of Afrin, the one tens of thousands of people used to escape the assault. We can't get to them or to the people buried under the rubbles of their homes," Avrin Hospital General Manager Dr. Jawan Muhammed told CNN.
Many hospital workers fled to areas where medical staff are aiding refugees. A small team stayed behind at the hospital.
"But most of the hospital was burnt," Muhammed said.
Turkey denied that it bombed the hospital and released a video Saturday that officials said shows a building in good shape.
"It is closely being monitored that vile propaganda against the Turkish armed forces is being spread, falsely claiming that buildings and vehicles were set ablaze by the Turkish military. In reality it was being carried out by terrorists in Afrin city center," the statement said, according to Anadolu.
The hospital general manager told CNN the images that Turkey released show only part of the hospital complex, not the main building that was hit. A building containing the emergency facilities was severely damaged, Muhammed said.