BEIRUT — Doctors in Syria’s rebel-controlled suburbs of Damascus said Wednesday that they were unable to keep up with the staggering number of casualties, amid a ferocious bombing campaign by government forces that has targeted hospitals, apartment blocks, and other civilian sites, killing and wounding hundreds of people in recent days.

The bombardment forced many among the nearly 400,000 residents to sleep in basements and makeshift shelters and overwhelmed rescue workers who have spent days digging out survivors from the wreckage of buildings.

The Britain-based Syrian Observatory for Human Rights, which closely monitors the fighting through activists on the ground, said at least 300 people have been killed since Sunday night alone. The dead included 10 people killed in a new wave of strikes Wednesday on the town of Kafr Batna. Another 878 people have been wounded, mostly in airstrikes hitting residential areas, according to the UN human rights office.

Dr. Waleed Awata described a desperate, chaotic scene at the small hospital where he works as an anesthesiologist in the town of Zamalka, one of a cluster of settlements that make up the Damascus suburbs known as eastern Ghouta. The facility, with just 17 beds, received 82 patients on Tuesday night alone, he said.

‘‘We had to give them IVs and treat them on the floor,’’ the 44-year-old physician said. The bodies of two women and two children killed in Wednesday’s shelling were also brought to the hospital.

The hospital was struck Tuesday by barrel bombs — crude, explosives-filled oil drums dropped from helicopters at high altitudes — as well as sporadic artillery fire, Awata said. Like many hospitals in the area, patients had been moved into the basement to shield them from airstrikes. No one was hurt but the hospital’s generator, water tanks, and several ambulances were damaged.

Another doctor said he, too, was at the hospital where he works in the town of Saqba when it came under attack Tuesday, killing some of the patients and forcing others to be moved to nearby homes because the airstrikes made it too dangerous to take them to other hospitals.

‘‘By God, I am exhausted in every sense of the word,’’ said the physician, who spoke on condition of anonymity because he feared for the safety of relatives in government-controlled areas of Damascus.

The international medical organization Doctors Without Borders said 13 hospitals and clinics that it supports have been damaged or destroyed over the past three days. The International Committee of the Red Cross called for immediate access to tend to the wounded, saying medical personnel in the rebel-held areas were unable to cope amid shortages of medicines and supplies.

Syrian government forces supported by Russian aircraft have shown no signs of letting up their aerial and artillery assault on eastern Ghouta.

The doctor in Saqba said he had returned home Tuesday to rest after two back-to-back days of treating the wounded when a barrage of rockets landed in his neighborhood, shaking his apartment and breaking the windows.

Minutes later, the airstrikes began. The first one hit his house, the doctor said, adding that he couldn’t see anything through the dust as he called out to his pregnant wife and two young children, ages 2 and 1. Neighbors came to their rescue and helped them evacuate to the basement, where they spent the night. They suffered only superficial wounds.