(Adds Syrian state TV report of second rebel evacuation deal)
BEIRUT, March 23 (Reuters) - Syrian rebels agreed to surrender a second besieged enclave in eastern Ghouta on Friday, state television reported, as their comrades in another insurgent pocket in the area continued their withdrawal after a month-long assault by the army.
Capturing eastern Ghouta, near the capital Damascus, would be Syrian President Bashar al-Assad's biggest victory over the rebels since driving them from Aleppo in December 2016.
His army's month-long attack on the enclave has splintered it into smaller besieged pockets, seizing most of its area and, according to a war monitor, killing more than 1,600 people.
Insurgents in one of those pockets - the town of Harasta - began withdrawing in a convoy of buses for opposition territory in northwestern Syria on Thursday. More buses began to leave on Friday carrying fighters and their family members.
Syrian state television broadcast their departure. From behind a half-drawn curtain, a woman in a headscarf could be seen gazing out through a spiderweb of bullet holes and cracks in the window of a bus as it prepared to carry her into exile. A small child peered through another window.
Meanwhile, state television cited its own correspondent as reporting that rebels in a second pocket around the towns of Arbin, Jobar, Zamalka and Ein Terma had also agreed to leave.
About 7,000 people would exit those areas including fighters carrying light weapons, while people who chose to stay would settle their affairs with the government, it reported.
The spokesman of the dominant Failaq al-Rahman rebel group there, Wael Alwan, had earlier said it was negotiating with the government's ally Russia. "Today is a session to find a solution to end this human suffering, whatever the cost," he said on television.
But bombs still fell on Friday on the most populous rebel-held area in eastern Ghouta, the besieged city of Douma, from which thousands of people have fled into government territory in recent days.
After insurgents have surrendered the other two pockets, it will stand as the last battered and besieged rebel area in eastern Ghouta, itself the opposition's last major bastion near the capital.
The Syrian army's assault to recapture the area has been one of the most intense in the seven-year war.
It has been marked by tactics the army and its ally Russia have increasingly used to crush resistance - lay siege to an area, bombard it, launch a ground assault and finally offer the rebels and their families safe passage to the northwest.
After helping turn the tide of the war in Assad's favour with air power and military support since its intervention in 2015, Russia has increasingly cast itself as a peace-broker. Russian representatives have played a role in negotiating local ceasefires and evacuations.
Assad and his allies say their offensive in eastern Ghouta is necessary to end the rule of Islamist militants over the area's people, and to stop them shelling government areas.
Rebel rocket fire has killed scores of people during the army offensive on eastern Ghouta, state television has reported including in a strike that hit a market place on Tuesday.
A source in the Syrian Arab Red Crescent agency said four of its members, as well as other civilians, were injured on Friday by an explosion in Harasta. The war monitor, the Syrian Observatory for Human Rights, said the blast was caused by rebels detonating their arsenal before departing.
State television reported that 15 buses had left so far on Friday carrying 882 people, including 283 fighters. Around 1,500 people left Harasta on Thursday evening and reached the rebel-held northwest on Friday, the Observatory said.
In the rebel pocket in the southern part of eastern Ghouta, Failaq al-Rahman had announced its intention to negotiate on Thursday, when Alwan said a ceasefire had been agreed.
The Observatory said negotiators left the enclave late Friday morning as guns fell silent after air strikes and advances by pro-government forces had continued past the midnight ceasefire deadline.
State television broadcast footage of what it says was about 3,400 people leaving Douma on foot on Friday morning, carrying small children and belongings. Thousands of civilians have made the same journey over the past week, making their way to reception centres in government-held territory.
They were leaving behind them a blast-wrecked landscape of smashed concrete and twisted metal, where for weeks people have cowered in basements from the unrelenting bombardment.
Already besieged for years, people in eastern Ghouta have suffered acute shortages of food and medicine, and during the weeks-long battle they were often unable to leave their homes even to bury the dead.
The United Nations estimates more than 50,000 people have left besieged areas of eastern Ghouta in the past almost two weeks.
The Observatory estimates that in all, about 120,000 civilians have either left the enclave or remained in the towns of Kafr Batna and Saqba, which were re-taken by the government in the past eight days. (Reporting by Lisa Barrington and Angus McDowall, editing by Angus MacSwan)