Syrian rebel group Jaish al-Islam has agreed to evacuate jihadist fighters being held in its prisons in besieged Eastern Ghouta, a statement says. Government attacks there have killed almost 800 civilians since February 18.
Rami Abdurrahman, who heads the Britain-based Syrian Observatory for Human Rights, said Douma was shelled before the convoy went in.
The limited operation came as the powerful Jaish al-Islam said HTS fighters would be evacuated to the northern province of Idlib, in an arrangement struck following consultations with the United Nations and other global players.
The aid was delivered as helicopters hovered overhead and warplanes targeted areas outside Douma, a correspondent said. He also says that "a part of the medical and health supplies to be included for delivery was removed by the Syrian authorities".
The enclave's 400,000 inhabitants have been living under government siege since 2013, with food and medicines in very short supply even before the latest assault.
A United Nations official who entered eastern Ghouta earlier this week said civilians stuck inside the enclave - mostly women and children - would like to leave have nowhere to go and feel they can't exit safely from the designated checkpoints.
Friday's convoy included 2,400 food parcels for 12,000 people.
The Syrian opposition has accused Russian Federation of "taking revenge" for the failure of the Sochi Conference by widening the circle of death and destruction.
"I don't want to leave, but I don't want any harm to happen to my family", said Abu Ahmad al-Ghoutani, who said he has two children.
A negotiator from the Hammuriyeh said a "civilian delegation" wanted to hold talks with the regime to end the fighting in the area.
A tribal leader said more than 300 civilians from the areas of Kafr Batna, Saqba and Hammuriyeh wanted to leave.
He told journalists there had also been discussions for "500 fighters to hand over their weapons to the army". Washington intends to use the presence of the SDF and 2,000 United States special forces embedded with the SDF to weaken the government and provide the USA with leverage in peace talks.
The air and ground assault has left medical staff exhausted.
Doctors and nurses in the enclave have run out of several life-saving items, according to Doctors Without Borders (MSF).
Russian President Vladimir Putin ordered daily humanitarian pauses to be introduced in Eastern Ghouta from 09:00 to 14:00 local time from February 27.
In less than two weeks, the Syrian army has retaken almost all the farmland in eastern Ghouta under cover of near ceaseless shelling and air strikes, leaving only a dense sprawl of towns - about half the territory - still under insurgent control.
The onslaught has killed more than 1,000 people, the medical charity Medecins Sans Frontieres (MSF) said on Thursday.
UN High Commissioner for Refugees Filippo Grandi on Friday called the conflict a "colossal human tragedy".
"The conditions faced by civilians inside Syria are worse than ever, with 69 percent languishing in extreme poverty", he said.
On February 24, the UN Security Council in a unanimous vote approved the resolution demanding a 30-day ceasefire across Syria to allow aid access to the population.
The US seeks to maintain a foothold in Syria through its ally, the Kurdish-dominated Syrian Democratic Forces (SDF), which now occupies about 25 per cent of Syrian territory in Raqqa and Deir Ezzor provinces.