* Rebel advances elsewhere are slow and costly
* Tension under surface in Gaddafi-held mountain town
* Cameron, Rasmussen try to calm NATO discord
* Ex-Gaddafi advisor says Libyan leader playing for time
(Adds reporting from town of Gharyan)
By Nick Carey
GHARYAN, Libya, June 15 (Reuters) - Libyan rebels pushed deeper into government-held territory south of the capital on Wednesday, but their advance came as strains began to emerge in the Western alliance trying to topple Muammar Gaddafi.
Fighters in the Western Mountains, a rebel stronghold about 150 km (90 miles) south-west of Tripoli, built on gains made in the past few days by taking two villages from which pro-Gaddafi forces had for months been shelling rebel-held towns.
The rebels are still a considerable way from Gaddafi's main stronghold in Tripoli, while their fellow fighters on the other two fronts -- in Misrata and in eastern Libya -- have made only halting progress against better-armed government troops.
"The revolutionaries (rebels) now control Zawiyat al-Babour and al-Awiniyah after pro-Gaddafi forces retreated this morning from the two villages," Abdulrahman, a rebel spokesman in the nearby town of Zintan, told Reuters.
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In Gharyan, a Gaddafi-held town that forms the gateway from Tripoli to the mountains, there was an undercurrent of tension as the frontline moves closer to the capital. Libyan government minders brought a group of reporters to the town, which lies about 120 kilometres southwest of Tripoli and about 20 kilometres east of Kikla, which rebels seized from Gaddafi loyalists on Tuesday.
Despite an outward appearance of normality, numerous walls around town on Wednesday had recently painted over graffiti. The windows of one government building were smashed, the sign for another was riddled with holes.
While many traders and people on the streets were reluctant to talk to reporters, one shop owner said the calm in the area during the day was replaced by fighting every night.
"Two thirds of the people here are for the rebels," he told Reuters, giving his name as Mohammed.
Those willing to talk in front of the minders were strongly pro-Gaddafi.
"Sarkozy is stupid, he is fighting this war for petrol," a man called Yunis said in French, referring to the French president, villified by Gaddafi supporters as the driving force behind NATO bombing. "This is colonialism all over again."
The NATO military alliance, which has been pounding Gaddafi's military and command-and-control structures for nearly three months, has failed to dislodge him.
Libyan TV said on Wednesday a NATO bombardment had killed 12 people in a convoy in Kikla. A NATO official denied it.
TIME ON OUR SIDE
Ties are becoming strained in the alliance, with some NATO members complaining that others have been reluctant to commit additional resources needed to sustain the bombing mission in the coming months. [ID:nLDE75E0GG]
Adding to the pressure, Republicans in the U.S. Congress are pressing President Barack Obama to explain the legal grounds on which he was keeping U.S. forces involved in Libya without the authorisation of Congress.
Speaking in London after meeting NATO Secretary General Anders Fogh Rasmussen, British Prime Minister David Cameron reiterated that time was running out for Gaddafi and that the alliance was as determined as ever.
"I think there is a very clear pattern emerging which is time is on our side, because we have the support of NATO, the United Nations, the Arab League, a huge number of countries in our coalition and in our contact group," he said.
Rasmussen echoed those comments despite senior NATO commander General Stephane Abrial on Tuesday raising questions about the alliance's ability to handle a long-term intervention.
"Allies and partners are committed to provide the necessary resources and assets to continue this operation and see it through to a successful conclusion," Rasmussen said.
Russia's envoy to NATO, Dmitry Rogozin, said the alliance was "sliding down and being dragged more into the eventuality of a land-based operation in Libya".
In a theatrical show of defiance, Gaddafi was shown at the weekend playing a game of chess with a Russian official, but after weeks of ambivalence, Moscow has joined Western countries this month in calling for Gaddafi to step down.
Saad Djebbar, a former legal adviser to the Libyan government, told Reuters Gaddafi would continue to play for time and seek to demoralise and split the coalition.
"Gaddafi's mentality is that as long as my enemies haven't triumphed, I haven't lost," he said.
"The U.S. stance, that the major outside role should be played by the Europeans and Arabs, sends the wrong signal. Gaddafi will be very encouraged by it. His line is 'We are steadfast. We can wait it out.'"
Gaddafi has said he has no intention of leaving the country -- an outcome which, with the military intervention so far failing to produce results, many Western policymakers see as the most realistic way out of the conflict.
The Libyan leader has described the rebels as criminals and al Qaeda militants, and called the NATO intervention an act of colonial aggression aimed at grabbing Libya's oil.
Though under attack from NATO warplanes and rebel fighters, Gaddafi's troops have showed they are still a potent force.
A rebel spokesman in Nalut, at the other end of the Western Mountains range from Zintan, said Gaddafi's forces had been shelling Nalut and the nearby border crossing into Tunisia. The rebels depend on that crossing to bring in supplies.
On Tuesday, the rebels tried to advance in the east of Libya, setting their sights on the oil town of Brega, but they were unable to break through.
In Misrata, Libya's third-biggest city about 200 km (120 miles) east of Tripoli, rebels have been inching slowly west towards the neighbouring town of Zlitan along the coast road to Tripoli, but have repeatedly had to fall back under fire.
The rebels there have expressed frustration that NATO is not more active at taking out Gaddafi's forces there, and is not doing more to coordinate with fighters on the ground.
A Reuters correspondent in Misrata said there were no further advances towards Zlitan on Wednesday.
Austrian Foreign Minister Michael Spindelegger will visit the rebels in Benghazi on Sunday to offer "concrete support", his office said, the latest in a series of such visitors. (Additional reporting by Joseph Nasr in Berlin, Souhail Karam in Rabat, David Brunnstrom in Brussels, Mohammed Abbas in London, Hamid Ould Ahmed in Algiers, Nick Carey in Tripoli, William Maclean in London, Sylvia Westall in Vienna, Maria Golovnina in Benghazi, and Sami Aboudi in Cairo; writing by Tim Cocks and Christian Lowe; Editing by Peter Graff)