Syria talks bring offer of exit from siege of Homs GENEVA (Reuters) - The Syrian government said women and children could leave the besieged rebel city of Homs on Sunday as negotiators from the warring sides discussed humanitarian gestures on a second day of face-to-face talks in Geneva. Government and opposition delegates also spoke of releasing prisoners and enabling access for aid convoys during what the U.N. mediator acknowledged was a slow process but one which he hopes will lead on Monday to broaching the central issue that divides them after three years of civil war - namely Syria's political future and that of President Bashar al-Assad. Homs, occupying a strategic location in the center of the country, has been a key battleground. Assad's forces retook many of the surrounding areas last year, leaving rebels under siege in the city center, along with thousands of civilians. Syrian Deputy Foreign Minister Faisal Mekdad told a news conference after Sunday's meetings that the government would let women and children leave the city center if rebels gave them safe passage. U.N. mediator Lakhdar Brahimi said he understood that they would be free to quit Homs immediately. Mekdad said: "If the armed terrorists in Homs allow women and children to leave the old city of Homs, we will allow them every access. Not only that, we will provide them with shelter, medicines and all that is needed. We are ready to allow any humanitarian aid to enter into the city through the ... arrangements made with the U.N. In the city itself, however, opposition activists said rebels demanded a complete end to the blockade and opposed a limited ceasefire. An online video showed demonstrators with Islamist flags denouncing the Geneva talks as "treachery." Brahimi, who presided on Saturday over the first direct meeting between the two delegations, met both together again on Sunday morning, before holding discussions with each side separately in the afternoon. At another joint session on Monday, he hopes to begin discussion of a U.N. plan for a transitional government. Acknowledging the slow start to proceedings which began with a formal international conference on Wednesday, Brahimi said: "This is a political negotiation ... Our negotiation is not the main place where humanitarian issues are discussed. But I think we all felt ... that you cannot start a negotiation about Syria without having some discussion about the very, very bad humanitarian situation that exists. There was little sign of a softening of positions on the core issue - whether or not Assad should quit now, as the opposition and their Western and Arab backers say was agreed by a U.N. conference at Geneva 18 months ago. "The president of the Syrian Arab Republic stays until the Syrian people says something else," said Mekdad, repeating the government position that Assad can stay and win an election. For the opposition, spokesman Louay Safi said Monday's session with Brahimi would show if the government was willing to negotiate: "Tomorrow we start talking about transition from dictatorship to democracy. The regime is ... stalling. Brahimi said opposition delegates, who have asked for the release of nearly 50,000 detainees, had agreed to a government request to try to provide a list of those held by armed rebel groups - though many of these groups, fighting among themselves, do not recognize the negotiators' authority. Mekdad said the government had examined an opposition list of 47,000 people believed to have been arrested by Assad's forces and found most had either never been held or were now free. He also denied that any children were being held. Russian Foreign Minister Sergei Lavrov, whose government has helped Assad resist Western pressure but backs a negotiated peace to prevent the conflict spreading, called for progress on aid, unblocking besieged areas and prisoner exchanges. "All this would strengthen trust and affect the atmosphere at the talks in Geneva," he said in comments posted on the Foreign Ministry's website. Beyond this, it is very difficult to make guesses; the situation is extremely grave, positions are polarized, emotions are on the edge. Underlining the difficulty of implementing even local agreements on the ground, a U.N. agency trying to deliver aid to a besieged rebel area of Damascus said state checkpoints had hampered its work, despite assurances from the government that it would allow the distributions. An adviser to Assad, Bouthaina Shaaban, complained that opposition delegates were focusing on local issues and said the U.N. text calling for a political transition should be amended. The government was ready to discuss the Geneva Communiqué agreed by world powers 18 months ago, she said. But she added: "Geneva is not the Koran. It's not the Gospel ... In the summer of 2012, rebel forces took control of much of Aleppo, Syria's biggest city, and were challenging Assad's forces on the edge of Damascus. Since then, backed by Lebanese Hezbollah fighters and Iranian military commanders, Assad's forces have halted the rebel advances and consolidated control over the center of the country, although there is little sign of them retaking swathes of rebel-held territory in the east. Syrian Information Minister Omran Zoabi said there was no chance of Assad surrendering power: "If anybody thinks or believes that there is a possibility for what is called the stepping down of President Bashar al-Assad, they live in a mythical world and let them stay in Alice in Wonderland." There are now hundreds of rebel groups across the country, including al Qaeda-linked militants whose presence discouraged Western governments from backing the rebellion more forcefully. Few fighters heed the opposition in exile and the powerful Islamic Front has said negotiators who leave Geneva without having assured Assad's downfall will be treated as traitors. There was more fighting on Sunday, both between government and rebel forces and between Islamist rebels and ethnic Kurds, who have carved out their own territory in the northeast. The British-based Syrian Observatory for Human Rights said at least 26 fighters had been killed in clashes since Saturday between Kurds and Islamists. Additional reporting by Erika Solomon, Mariam Karouny, Dominic Evans, William James and Steve Gutterman; Writing by David Stamp and Alastair Macdonald; Editing by Andrew Heavens