Women and children trapped in the city of Homs have been allowed to leave immediately under a deal that marked the first tangible, if limited, sign of progress at the Syria peace talks in Geneva.

Lakhdar Brahimi, the Algerian diplomat representing the UN and Arab League, acknowledged that the agreement on Homs fell short of his hope to send a humanitarian aid convoy through to a rebel-held area of the central Syrian city, but, he said, "to bring Syria out of the ditch in which it has fallen will take time".

Brahimi defended the pace of the talks, which have yet to touch upon the issue of Assad's future. "I think being too slow is a better way than going too fast," he said. "If you run, you may gain one hour and lose one week."

Brahimi said on Saturday that the negotiations between Syrian government and opposition representatives had got off to a "good beginning", but said the two sides were speaking only through him and not directly to each other.

In Sunday's first session the format was the same. In the afternoon the teams convened in separate rooms at the UN HQ, with the veteran mediator shuttling between them.

Munzer Aqbiq, spokesman for the western-backed Syrian Opposition Coalition (SOC), accused Assad of stalling on the Homs aid convoy. Buthaina Shaaban, the president's media adviser, said the matter was being dealt with in Damascus. Western diplomats said the official Syrian delegation had denied knowing about the relief plan – which was drawn up with input from the US and Russia, as well as the UN and Red Cross – when it was raised.

Opposition representatives had earlier signalled that they would demand the release of 50,000 detainees held by the government, including 2,500 women and children. Omar al-Zoabi, Syria's information minister responded: "We must be precise about the prisoners question. There are also thousands of people who have been kidnapped, some who have been missing without a trace for two and a half years."

The Geneva process, launched at a grand international conference in nearby Montreux last week, has already settled into a set routine. Spokespeople from both sides emerge regularly from the UN's Palais des Nations to give TV interviews in the beautifully tended gardens overlooking Lake Geneva and the snow-capped Alps. The aim is to get their messages across and to discredit each other.

Asked for his response to the latest position taken by the SOC, Zoabi replied scornfully: "They make so many statements I don't have the time to follow them."

Some of the sharpest exchanges have been between journalists working for government-approved media and opposition representatives. In the evenings, western officials and advisers working with the anti-Assad camp hold briefings in one of Geneva's most exclusive hotels.

Western diplomats argue that it is vital to move quickly from discussing confidence-building steps to the heart of the internationally backed Geneva I agreement of June 2012 – the creation of a transitional governing body. That is supposed to happen by mutual consent, even though it is clear that Assad's future is the main problem. Brahimi said on Sunday, this potentially explosive issue would not be tackled until Monday at the earliest.

The Syrian government is clear about its objections. "It is a big lie that this is about the president," Shaaban said. "Is this about the government or about the destruction of Syria? That's what they [the opposition] want. We are here in good faith. We want to stop this horrible inferno that is making our lives hell. We want the best for Syria.

"These people represent only themselves. They represent only a small fraction of the opposition who have not been living in Syria. I do not want to talk about transition while my people cannot have food and medicine and while children are being killed and kidnapped. What I want is to restore peace and security and then we will talk about a political process. Our priority is to stop terrorism."