One hundred buses carrying 6,749 people - around a quarter of them fighters - left a part of the enclave controlled by the Faylaq Al Rahman rebel faction, the Sana state news agency said.
Separately, he mentioned the forthcoming April 4 summit between Turkey, Iran and Russia in Istanbul, which Yuva said would "give a new dimension to the process of Syrian settlement against the backdrop of the development and strengthening of Russian-Turkish cooperation on Syria".
The largest convoy of evacuated militants and their families has departed Syria's Eastern Ghouta as the Syrian army presses ahead with a counterterrorism operation in the suburban area near Damascus.
Douma-based activist Laith al-Abdullah told Al Jazeera that Faylaq ar-Rahman are trying to evacuate their extended family members now trapped in Douma - despite ongoing negotiations.
Almost 1,000 people - including rebels, their relatives and other civilians - were evacuated on Saturday, followed by 5,435 people on Sunday.
Moscow has negotiated two evacuation deals so far for Ghouta.
President Bashar al-Assad has used such agreements to recover swathes of territory since the uprising against him began seven years ago this month.
The regime responded with a crippling half-decade siege on the suburb's 400,000 residents, sealing off access to food, medicine and other goods.
Heavy Snow Misses Twin Cities, Few Flurries Expected Saturday
Roads for the most part are wet, but watch for slushy spots, as well as very low visibility as heavier snow bands move through. Accumulations of 8 to 10 inches of sleet, slush and snow is expected within the warning area with locally higher amounts.
According to activists, a deal between the Jaish al-Islam rebel group and the Russians will most likely be announced at the end of the week.
On February 18, the regime, its ally Russian Federation and loyalist militia launched an all-out air and ground assault that killed more than 1,600 civilians, according to the Syrian Observatory for Human Rights.
The deal also demands the rebels to set free people they have previously kidnapped.
Eastern Ghouta, a 105-square-km agricultural region consisting of several towns and farmlands, poses the last threat to the capital due to its proximity to government-controlled neighborhoods east of Damascus and ongoing mortar attacks that target residential areas in the capital, pushing people over the edge.
Some 200,000 people are estimated to remain in Douma, including many who fled other parts of Ghouta as regime forces advanced.
It said a "preliminary understanding" had been reached that would see the "dissolution of Jaish al-Islam, the handover of its heavy weapons and the return of state institutions to the city".
"My mother's heart is broken from waiting", she says.Tens of thousands of Syrians have been reported missing in Syria since its civil war broke out in 2011 with the brutal repression of anti-government protests.