The largest convoy yet of armed fighters and civilians left a devastated pocket of Eastern Ghouta early on Tuesday, further emptying the onetime Syrian rebel bastion.
Government troops, backed by Russia and loyalist militia, launched a ferocious assault more than a month ago to retake the enclave on the outskirts of of Damascus.
They have recaptured more than 90 percent of it and are draining the last rebel-held pockets through negotiated withdrawals brokered by Russia.
Two such deals have already seen thousands of rebels, their relatives and other civilians bused out of bombed-out Ghouta districts to Idlib, a northwestern province most of which still escapes government control.
The largest numbers have quit the towns of Arbin and Zamalka, and the adjacent district of Jobar, all controlled by the Faylaq Al-Rahman Islamist faction.
The group reached a deal with Moscow on Friday and its implementation began the following morning with nearly 1,000 people boarding buses and leaving.
The numbers have grown steadily since, with the biggest convoy yet departing overnight after filling up all day under the supervision of Russian military police.
One hundred buses carrying 6,749 people — around a quarter of them fighters — left the Faylaq-controlled pocket in the early hours of Tuesday, state news agency SANA said.
That convoy brought the total number of evacuees from the pocket to 13,165 people, and more departures were expected later on Tuesday.
Faylaq Al-Rahman spokesman Wael Alwan has said as many as 30,000 people could be evacuated in all.