source said progress had been slow.
"Small steps, but small steps are better than no steps," the source said. "It's clear there will be hysterical episodes each day."
Humanitarian access for Homs, where insurgents in central districts are surrounded by Assad's forces, could be agreed quickly. Abdah said the opposition had already asked fighters on the ground to respect a ceasefire and to protect convoys of aid once the agreement is reached.
"We had a suggestion prepared for this before the conference began and already spoke about it to the Red Cross and countries that are close to the regime like Russia, as well as United States and the United Nations," he said.
The proposal, which includes granting civilians safe passage, could lead to a ceasefire in Homs city for a week or two, which if successful could be extended to the whole of the central province - a major battleground.
But profound mutual mistrust and the absence from Geneva of powerful Islamist opposition groups as well as Assad's ally Iran make any substantial progress very difficult, and previous ceasefires in Syria have proved short-lived.
The crisis flared with street protests against Assad's rule in March 2011 and descended into an armed insurgency and civil war after security forces put down demonstrations with force.
There are now hundreds of rebel brigades across the country, including hardline Islamists and al Qaeda-linked militants, few of whom pay much heed to the opposition in exile.
Abdah said the fact that Brahimi had raised the issue on Saturday, after separate talks with the opposition and government delegations a day earlier, meant the ceasefire idea had already won a degree of consensus between the two parties.
Brahimi had already indicated that his aim was to start by seeking practical steps, such as local ceasefires, prisoner releases and access for international aid deliveries, before embarking on the tougher political negotiations.
"I think an immediate political solution is unrealistic, unfortunately," French Foreign Minister Laurent Fabius told France 24 television.
Syria's civil war has made half of the 22 million population dependent on aid, including hundreds of thousands cut off by fighting.