Geneva, Switzerland (CNN) -- Hundreds of families starving in the besieged Syrian city of Homs may soon have a way out.
Syria's government has agreed to let women and children leave the old city of Homs. And other civilians "are also welcome to leave, but the government needs a list of their names first," the U.N. envoy leading talks between Syria's warring sides said Sunday.
"So hopefully, starting tomorrow, women and children will be able to leave the old city in Homs," Lakhdar Brahimi said. "And I hope that the rest of the civilians will be able to leave soon after that."
The government wants the list of names, Brahimi said, "so that they see that they are civilians, (that) they're not armed people."
It's a small step forward in talks in Geneva aimed at ending Syria's brutal civil war.
The stakes for an agreement are enormous. More than 100,000 Syrians have been killed in the conflict and more than 2 million people have become refugees. The conflict has also been deepened by accusations that the Damascus government used chemical weapons and that the opposition includes al Qaeda-affiliated groups.
A key topic on the table has been the delivery of food and medicine to Homs, which has been under siege for months.
Brahimi said Sunday that Syria's government was in the process of considering possibly allowing an aid convoy into the area.
Behind the scenes, diplomats and a senior U.S. official at the talks described the humanitarian situation in Homs as dire and said that the regime has been systematically stopping aid from reaching the city.
"The regime is blocking all convoys of aid to Homs and has been doing so for months," the official said. "The U.N., with the Red Cross, has been trying to get these aid convoys through to the city of Homs; the regime is blocking it. The situation is extremely urgent. Anything the regime says to the contrary is wrong."
It's still not clear how much promises made during Sunday's talks will impact life on the ground, a Red Cross official said Sunday.
"The political announcements just began. We need to see tomorrow how the talks will translate on the ground. We need to see tomorrow if the security is in place, if the roads are open," said Anastasia Isyuk, an International Committee of the Red Cross spokeswoman. "While this is a good sign, what is needed is access to Homs itself and humanitarian organizations like ourselves to be able to go in and assist people."
As for the talks in Geneva, Brahimi said Sunday that it's too soon to say how long they could last.
"I am often accused of being too slow, but I think that being slow is a better way of going fast. ... If you run, you may gain one hour and lose one week," he said. "So we are going slow. I hope that we will continue to be going slow. So far, I think that the process is continuing, but it's very early."
After several sessions negotiating face to face, the two sides moved into separate rooms Sunday.
Does that mean the talks are in trouble?
Not at all, Brahimi said.
"I think it's very useful," he told reporters. And on Monday, he said, he plans once again to meet with both sides together in the morning, and then separate them in the afternoon.
CNN's Nic Robertson and Alex Felton reported from Geneva. CNN's Catherine E. Shoichet reported from Atlanta. CNN's Samira Said, Marie-Louise Gumuchian, Michael Martinez, Chelsea J. Carter, Tom Cohen, Elise Labott, Gayle Edmonds and Saad Abedine contributed to this report.