Syria will allow women and children to leave the besieged area of Homs "from now", the UN mediator at the Geneva peace talks has told reporters.
Syrian Deputy Foreign Minister Faisal Mekdad said women and children were free to leave. He alleged armed groups were preventing them from leaving.
Mr Brahimi said that the opposition had agreed to give the government lists of detainees held by armed groups.
He said it was "too early" to assess the prospects of a comprehensive deal.
He admitted the talks were proceeding slowly but said that on Monday he "expected the two parties to make some general statement about the way forward".
This is a significant if limited development from the peace talks in Geneva: permission from the Syrian government to lift the siege on parts of the old city of Homs which for months had left hundreds of people trapped, including the very ill and very vulnerable.
Syrian Deputy Foreign Minister Faisal Mekdad also said his government was ready to allow any humanitarian aid into Homs but warned that that depended on rebel militia refraining from opening fire.
However, the opposition is still wary. They say they have guarantees from rebel fighters to observe a ceasefire, but it is still not clear the government can be trusted. "Yes, it would be progress to let out women and children," said Obeida Nahas, one of the opposition delegates in Geneva, "but we feel lists could be used to detain and torture people".
So both on the issue of letting out trapped civilians, and the hope that a UN aid convoy might be in Homs soon, there is a feeling there could still be last-minutes hitches. It is symptomatic of the lack of trust on both sides in Geneva that even one small humanitarian step is extraordinarily difficult to bring off.
Mr Brahimi said he hoped a humanitarian convoy from the UN and the Red Cross would be able to go to Homs on Monday.
Hundreds of people are reportedly trapped in besieged parts of the city, including some who are very ill.
If all goes well, the agreement on Homs would be the first concrete outcome of the peace process, the BBC's Bridget Kendall reports from Geneva.
Lists of names
Mr Mekdad said he hoped arrangements could be made with local officials to allow the convoy access but that the aid must not fall into "the hands of terrorists", the term Syrian officials use for all armed opposition.
Mr Brahimi said that the government would allow women and children to leave immediately but had asked for a list of adult male civilians who wanted to leave to ensure they were not fighters.
"You know that the centre of the city has been under siege for a very, very long time and now I hope that we are approaching a solution for at least the civilians," he said.
The envoy said the opposition had pledged to gather names of detainees from groups it had "authority over or contact with" but admitted that this did not include all anti-government groups fighting in Syria.
The opposition in turn has been asking for the release of thousands of prisoners in government detention.
Mr Brahimi said the talks in Geneva had taken the form of a joint session with the government and opposition in the morning before he met the sides separately in the afternoon.
He added that he expected this pattern to be repeated on Monday.
Mr Brahimi said he had been encouraged by the atmosphere at the talks on Sunday, saying they had been characterised by "respect and exchange".
No direct words had been exchanged between the delegations but the two sides were talking to each other through him, Mr Brahimi said.
Meanwhile, fighting continued unabated inside Syria.
The UK-based activist group the Syrian Observatory for Human Rights reported that the al-Qaeda-linked Islamic State in Iraq and the Levant (ISIS) had clashed with Kurdish groups in the north-east. The fighting between the two has killed 26 since Saturday, the group says.
As well as the continuing war between government and opposition, ISIS has clashed with several rival rebel factions in the north in recent weeks.
Syria's civil conflict has claimed well over 100,000 lives since it began in 2011.
The violence has also driven 9.5 million people from their homes, creating a major humanitarian crisis within Syria and for its neighbours.
The opposition and government are fundamentally divided over the aims of the conference.
The government delegation has said the main issue of the talks is finding a solution to foreign-backed "terrorism".
The opposition, however, had insisted that the regime commit in writing to the Geneva I communique, which called for a transition process.
The communique urged Syria to form a transitional governing authority that "could include members of the present government and the opposition and other groupshttp://www.bbc.co.uk/news/world-middle-east-25905465