The Syrian government said women and children could leave the besieged city and that rebels should hand over the names of the men who would remain but US State Department spokesman Edgar Vasquez said an evacuation was not an alternative to immediate aid.
He added: "The situation is desperate and the people are starving."
UN mediator Lakhdar Brahimi said he hoped the talks in Geneva could tackle the central issue that divides the two sides - Syria's political future and that of Mr Assad - but both sides immediately adopted entrenched positions.
Syria's government delegation presented a document for negotiation which did not mention a transition of power.
The opposition, which wants Mr Assad to quit as part of arrangements for a transitional government, immediately rejected the proposal.