Speaking ahead of the new Geneva round, United Nations mediator Staffan de Mistura urged all interested parties to support the talks set to be attended by the government delegation, headed by Syria's United Nations ambassador Bashar al-Jafaari and the HNC.
The opposition delegation will be represented by the Riyadh-based High Negotiations Committee and led again by Nasr al-Hariri and Mohammad Sabra.
De Mistura insisted the Geneva political talks had to be seen in tandem and not in conflictwith Astana, and that there was no solution to Syria's devastating six-year civil war without a political settlement on the horizon, the Guardian reported.
On Tuesday, HNC delegation head Nasr al-Hariri reiterated the opposition's stance that there can be no role for Assad in the political settlement, and supported the recent US accusation that the Syrian government built a crematorium at Saydnaya prison, according to the Local.
Hundreds of rebels and their families left Qaboun on Sunday and Monday, headed toward rebel-held areas, bringing all parts of the capital under the control of President Bashar Assad's forces for the first time since 2012.
But the HNC's Munzer Makhos said opposition figures had "many reservations" and were still discussing it.
This round will be shorter and more business-like, starting on Tuesday and ending by Saturday, and with less room for rhetoric, de Mistura said.
Mr Aron Lund, a fellow at The Century Foundation, said the Geneva talks were revolving around the "dead end" issue of Mr Assad and were not "moving forward in any visible way".
Hopes for a breakthrough remain dim, particularly after USA claims of new regime atrocities at the notorious Saydnaya prison near Damascus.
HNC spokesman Salem al-Meslet, speaking to AFP ahead of his delegation's first meeting on Tuesday, said the new accusations demanded a response. "These allegations are totally unfounded, they are nothing but the product of the imagination of this administration and its agents", state news agency SANA quoted the foreign ministry as saying. "The Americans know what's going on in Syria now", Muslet said.
Agreements reached in previous rounds of talks between the warring sides will be discussed in the scope of a four-part agenda. "We need to see Russian Federation help Syrians decide their fate and their destiny", said HNC spokesman Salem Al Meslet.
United Nations officials said Monday that they had reason to believe the current Geneva talks would be more substantive than previous ones.
Although Syrian president Bashar al-Assad recently dismissed the talks as "fruitless", de Mistura pointed out that the government delegation was in Geneva and "is ready to work".
Assad said he was more interested in the plans for de-escalation zones set out by Turkey, Russia and Iran at separate talks held in the Kazakh capital Astana.
One newly released image, a commercial satellite photograph dating back to January 2015, shows snow melting on the roof of a building attached to the Saydnaya military complex north of Damascus.