(Adds further comment)
* Mediator says US, Russia pledge to held peace talks
* "Failure is always staring us in the face," he says
* Russia presents U.N. resolution, counter to West
* Homs ceasefire extended until Saturday
By Stephanie Nebehay and Tom Miles
GENEVA, Feb 13 (Reuters) - Warning that "failure" was staring him in the face, the Syria peace talks mediator said on Thursday that the United States and Russia had promised renewed support to keep their rival Syrian allies talking.
U.N. diplomat Lakhdar Brahimi met senior diplomats from Washington and Moscow in Geneva, hoping the co-sponsors of the three-week-old negotiating process could bury their own deep differences over Syria and prevail respectively on the opposition and government to move ahead and compromise.
"They have kindly reaffirmed their support for what we are trying to do and promised that they will help both here and in their capitals and elsewhere to unblock the situation for us, because until now we are not making much progress in this process," Brahimi told a news conference.
Asked after his two-hour meeting with U.S. Under Secretary of State Wendy Sherman and Russian Deputy Foreign Minister Gennady Gatilov whether the whole process had failed, he said:
"Failure is always staring at us in the face.
"As far as the United Nations is concerned we will certainly not leave one stone unturned if there is a possibility to move forward. If there isn't, we will say so."
A U.S. official said: "The hard work of this diplomacy continues and the United States will continue to support this work." Russian officials were not immediately available.
Opposition spokesman Loay al-Safi said Brahimi's efforts were "welcome" but without progress in talks, the opposition would "demand" the U.N. Security Council "make a stand". Syrian government delegates were not immediately available to comment.
A new standoff between Russia and the West in the Security Council, over resolutions on aid for Syria, has contributed to the deadlock in Geneva, while continuing fighting has left tens of thousands under siege and hoping for relief from abroad.
Russia said it had presented a draft U.N. resolution on fighting "terrorism" in Syria and its own plan for improving aid access, throwing down a challenge to Western states in the Council which proposed another formulation that Moscow says would open the way for Western military intervention.
In Geneva, where the second round of peace talks has made little progress since Monday, Western diplomats and the Syrian opposition delegates have complained that President Bashar al-Assad's government was refusing to discuss proposals for a transition of power and hoped Russia would press it to do so.
"What we have seen so far is that the regime is not serious," opposition delegate Anas al-Abdah said. "The sooner the Russians can put enough pressure on the Syrian regime side, the better. And they are positioned to do that."
Western diplomats also said they hoped Moscow could apply pressure on the Damascus government to do more to compromise. If not, some feared a third round of talks might not follow any time soon after this week's discussions wind up.
Several delegates said it was unclear on Thursday evening even whether talks would continue as planned on Friday.
Opposition activists say the rate of killing has increased in the three weeks since talks began - averaging a record of more than 230 a day - as both sides have sought to shore up their bargaining positions by gaining territory.
On Thursday, activists said government forces dropped crude barrel bombs from the air on rebel-held areas around Damascus and Aleppo, as well as the town of al-Zara near Homs. There were clashes in Hama province near a highway that rebels have been trying to block to cut the government's supply lines.
Russia has been Assad's most powerful international ally during the three-year-old conflict, using its veto in the Security Council to block bids to pressure him with condemnation or the threat of sanctions.
U.S. President Barack Obama criticised Russian attitudes to the latest U.N. efforts to provide aid. The Russian Foreign Ministry hit back on Wednesday, calling that a "distortion".
Moscow's new push for a resolution condemning acts of "terrorism" is in tune with rhetoric from Damascus, which uses the term to describe all those fighting to oust Assad in the conflict that has killed more than 130,000 people.
The Syrian government delegation has resisted efforts to discuss a transition of power in Geneva this week, saying fighting "terrorism" must be addressed first.
"Terrorism is certainly no less acute a problem" than the humanitarian crisis in Syria, Russian Foreign Minister Sergei Lavrov told a news conference in Moscow. He added that "terrorist groups" fighting there were a growing threat.
In Homs, a key battleground, the evacuation of hungry civilians and rebel fighters from the besieged old city was continuing for a seventh day and a ceasefire was extended until Saturday evening, the governor said.
In all, 1,400 people had been evacuated since Friday, when a U.N.-brokered ceasefire came into force, the only practical achievement of the Geneva process begun on Jan. 22.
Of these, 220 were still being detained for questioning. While women and children have been free to leave, men and youths aged between 15 and 55 are deemed of fighting age by the Syrian authorities and are being vetted by the security forces.
A U.S. State Department spokesman said on Wednesday that the government had pledged to release men after screening.
Amnesty International urged the U.N. Security Council to overcome its differences and act to help the up to a quarter of a million Syrian civilians stuck under siege.
Survivors from Homs told of cigarettes costing $30 a pack and of food being unobtainable. Some spoke of people dying after foraging poisonous weeds. One man said he had cooked and eaten a cat, adding: "It tastes like any other meat." (Additional reporting by Khaled Yacoub Oweis and Oliver Holmes in Geneva, Steve Gutterman and Gabriela Baczynska in Moscow, Erika Solomon in Beirut and a reporter in Homs; Writing by Alastair Macdonald; editing by David Stamp)