* Mediator does not expect progress by end of session on Friday
* Talks to work on 2012 Geneva communique, but approaches differ
* Government wants to focus on "terrorism", opposition on political transition
* Humanitarian relief for Old City of Homs still deadlocked
By Khaled Yacoub Oweis and Mariam Karouny
GENEVA, Jan 29 (Reuters) - International mediator Lakhdar Brahimi said on Wednesday that he does not expect to achieve anything substantive in the first round of Syria talks ending on Friday, but hoped for a more productive second round starting about a week later.
His sombre assessment came as the two sides took a first tentative step forward by agreeing to use the same 2012 roadmap as the basis of discussions to end the three-year civil war, though they disagreed about how talks should proceed.
"We talked about the TGB (Transitional Governing Body), but of course it is a very, very preliminary discussion and more generally of what each side expects," Brahimi told reporters.
Asked his expectations for the first week-long round expected to end on Friday, he said: "To be blunt, I do not expect that we will achieve anything substantive.
"I am very happy that we are still talking, but the ice is breaking slowly. But it is breaking," he said, adding that he was not disappointed.
Opposition and government sides said they agreed to use the "Geneva communique", a document endorsed by world powers at a conference in June 2012, and which sets out the stages needed to end the fighting and agree on a political transition.
"We have agreed that Geneva 1 is the basis of the talks," opposition spokesman Louay al-Safi told reporters.
The Syrian government delegation, which had earlier submitted its own document that it wanted the talks to focus on, said it would use the Geneva communique, with reservations. Syrian state television said the government wanted to discuss the text of Geneva 1 "paragraph by paragraph".
While the opposition wants to start by addressing the question of the transitional governing body that the talks aim to create, the government says the first step is to discuss "terrorism".
There was still no sign of a breakthrough in attempts to relieve the suffering of thousands of besieged residents of the rebel-held Old City of Homs, an issue that had been put forward to break the ice and build confidence at the start of the talks.
"We also tried to see what is happening over the humanitarian issues, in particular about Homs. Negotiations between the United Nations and the Syrian authorities are still ongoing," Brahimi said of the stalled U.N. aid convoy.
"Mr Brahimi said tomorrow they are going to discuss terrorism because stopping terrorism is the first issue that should be handled," said Bouthaina Shaaban, an adviser to Syrian President Bashar al-Assad.
The Geneva communique refers to the government and "armed opposition groups", but there is no mention of "terrorism" or "terrorists", terms used by the Syrian government to describe those fighting to overthrow Assad.
The opposition delegation wants discussion of the transitional governing body to come first, including its size and responsibilities, Safi said.
"They seem to be more ready to discuss that issue, but still they are trying to push it to the back of the discussion. We told them this has to come first, because nothing else can be achieved unless we can form the transitional governing body."
The opposition says transitional arrangements must include the removal of Assad, which the government rejects.
Despite contradictory interpretations of Geneva 1 by the two sides, organisers of the talks at United Nations headquarters in Geneva have made it a priority to keep the process going and dissuade either side from walking out.
The absence from the talks of powerful Islamist groups opposed to Assad, and of Iran, Assad's main regional ally, has put a major question mark over what can be achieved.
The United States and Russia, the joint sponsors of the conference, agreed on Wednesday to increase pressure on the two sides to reach a compromise, Russia's state-run RIA news agency reported, citing an unnamed diplomatic source.
Brahimi said he was in touch with both powers and hoped that they would exert greater influence in the future.
A Western diplomat said it was positive that the parties were still at the table.
"We don't think this is a process that should last years, but it's clear that after three years of civil war, a week isn't going to resolve it," the diplomat said.
"What we hope is that by the end of the week there will be sufficient common ground so that they agree to meet again and hopefully something tangible comes out on the humanitarian side."
The opposition wants the government to allow in a U.N. aid convoy for 2,500 people under siege in the Old City of Homs, but the government has said it needs to be sure the food and medicine will not go to armed groups or terrorists.
"It is still stalled, as far as I know," said Patrick McCormick, spokesman of the U.N. Children's Fund (UNICEF).
A spokeswoman for the U.N. World Food Programme, which is waiting to deliver a month's rations to the Old City, devastated by shelling and fighting, also said there was no movement.
U.N. human rights chief Navi Pillay has previously said international law requires all sides to permit free passage of food and medicines, and starvation of civilians as a method of combat may amount to a war crime.
Access to Homs and other besieged areas holding an estimated 250,000 people is seen as a proving ground for the peace talks.
The government has encircled hundreds of thousands of people across Syria, blocking off food and medicine. Rebels have also besieged 45,000 people in two Shi'ite Muslim towns in the north.
The Syrian opposition is willing to lift a siege on three pro-government villages as part of a wider deal, its spokesman said on Tuesday.
Damascus has said women and children may leave the Old City of Homs but that it wants the opposition to provide a list of men seeking to do so, before they may leave, Brahimi said this week.
(Additional reporting by Stephanie Nebehay and Tom Miles in Geneva, John Irish in Paris and Stephen Kalin and Oliver Holmes in Beirut; editing by Giles Elgood and Will Waterman)