* Brahimi tries to increase pressure on delegates
* Plans separate talks for first few days of second round (Adds ceasefire appeal)
By Khaled Yacoub Oweis
GENEVA, Feb 10 (Reuters) - Mediator Lakhdar Brahimi will meet representatives of the warring sides in Syria separately for the first few days of a second round of talks that began on Monday and is urging them to commit to discussing core issues.
In a letter reviewed by Reuters on Monday, Brahimi increased pressure on the two sides to show willingness in a peace process sponsored by Moscow and Washington that made no progress in the first round.
He said he would talk to the two Syrian sides on their own for the next two to three days in hope of improving the negotiating atmosphere.
In the eight-page document, dated Feb 7, which was given by Brahimi to both delegations at the weekend, he asked them to make a commitment at the start to deal with the two main issues: stopping the fighting and working out how to establish a transitional governing body.
"The two issues are among the most complex and sensitive and both subjects need treatment over several sessions and long discussions," the document said.
"But the future of this political process and the possibility of its success require a clear declaration from the outset that the two parties have the full and strong political will to deal with these two issues."
With no agreement on which issue should be discussed first, and a case to be made that both depended on the other, Brahimi said he would take them together and discuss them in parallel.
During the second week of talks, he plans to expand the scope of the discussion to two other issues: how to manage the continuity of Syria's state institutions and how to handle the process of national dialogue and reconciliation that would arise from any eventual agreement in Geneva.
The first round had aimed to build confidence by focusing narrowly on trying to agree a humanitarian ceasefire in the devastated city of Homs but the truce was not finalised until afterwards and was broken soon after it began.
On its third day on Sunday, aid officials said they were working to extend it, even though aid convoys had come under fire as they evacuated people and were briefly trapped in the city.
Despite problems with the Homs deal, Brahimi appealed to the two sides to work out local ceasefires, adding that only a comprehensive deal in Geneva could put an end to the warfare.
"Will the two sides... starting on Feb. 10, contribute even at a minimum, toward lessening the manifestations of violence, stopping the use of certain weapons and reaching ceasefires in some areas, even for a short period?" the letter said.
(Editing by Tom Miles and Philippa Fletcher)