Agreement will move up to 1,500 people from Barza, as Syrian government nears full control of capital province
Syrian rebels and their families began evacuating from a district of Damascus for the first time on Monday, bringing the government closer to recapturing all of the capital.
The evacuation of Barza began days after regime backers Russia and Iran and rebel supporter Turkey signed a deal to implement "de-escalation zones" where the government and opposition will halt hostilities.
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Syria's foreign minister, Walid Muallem, on Monday rejected any role for United Nations or international forces in monitoring the zones.
The deal to evacuate Barza district mirrors similar agreements for opposition-held territory elsewhere, allowing fighters safe passage in exchange for surrender.
"Armed men and some of their families have begun leaving Barzeh on 40 buses heading towards northern Syria," state television said.
It added that the evacuation would continue for five days, but that rebel fighters who chose to stay could do so if they register with the government.
The channel did not specify how many people were expected to leave, but the Syrian Observatory for Human Rights monitor said up to 1,500 people - mostly rebels - would leave Barza today and head to the northwest province of Idlib.
The evacuation deal was struck late on Sunday night, and dozens of people gathered in Barza from Monday morning.
An AFP photographer saw rebel fighters carrying light weapons looking on as children and women in brightly-coloured headscarves pulled shabby suitcases and duffel bags.
Syrian opposition fighters and families prepare to flee Barzeh (AFP)
A source from the pro-government National Defence Forces said rebel fighters would be allowed to take their "personal weapons" with them.
Negotiations were ongoing for a similar deal in the district of Qaboun, in Damascus's northeast, which forces loyal to President Bashar al-Assad have been shelling heavily for weeks.
"We are working on Qaboun and there is the Yarmouk camp, where talks are under way for the evacuation of armed groups," Muallem said during a news conference Monday.
On Sunday, Hezbollah said a deal had been struck to evacuate wounded Nusra Front fighters from the Yarmouk camp, in the southern suburbs of Damascus, to rebel-held Idlib province.
The wounded fighters and some others accompanying them would form a group of about 50, reported Hezbollah's al-Manar television channel, which is based in Lebanon.
Hezbollah is a close military ally of Assad.