UPDATE 1355 GMT: United Nations envoy Lakhdar Brahimi has tried to maintain optimism, both over the talks and the humanitarian situation in Homs, despite no sign of advance on Tuesday:

UPDATE 1245 GMT: The opposition says this morning’s joint session was fruitless:

The Geneva II “peace” talks resumed on Monday, but were dominated by the trading of blame between the Assad and opposition delegations over attacks on humanitarian convoys trying to reach the besieged Old City of Homs.

At least five people were killed in the weekend’s mortars and gunfire. About 900 civilians were evacuated, while a limited amount of food parcels and flour finally was delivered.

United Nations envoy Lakhdar Brahimi (pictured) met the Assad and opposition delegations in separate sessions, with the latter warning that it would not return for more discussions if this week’s talks were fruitless.

“If there is no progress at all, I think it would be a waste of time to think about a third round,” Syrian National Coalition spokesman Louay Safi said.

Information Minister Omran al-Zoubi said the Assad delegation presented Brahimi with an account of a “massacre” in the town of Maan in Hama Province, captured by insurgents last week.

The two sides will sit in the same room with Brahimi on Tuesday morning.