* Ceasefire holding in oasis town of Sabha-Reuters reporters
* Prime minister meets representatives of warring sides
* Clashes underline fragility of Libya after Gaddafi
* Second stand-off in west of country (Updates with more PM quotes in paragraphs 12-13)
SABHA, Libya, April 1 (Reuters) - Libya's prime minister flew to a desert oasis city on Sunday to try to patch up a tribal dispute that has killed about 150 people over the past week and underscored the ethnic faultlines threatening Libya's stability.
A Reuters team that flew with the prime minister to Sabha, about 750 km south (450 miles) of the Libyan capital, said a ceasefire appeared to be holding between the Tibu ethnic group and the Sabha militias with which they had been clashing.
Smashed windows at a conference centre and burned-out vehicles in a Tibu-controlled neighbourhood bore testimony to the fighting over the past days, some of the worst since a revolt last year ousted Libyan leader Muammar Gaddafi.
Asked about the situation in Sabha, Prime Minister Abdurrahim El-Keib told Reuters: "It's much better than I thought."
He said he wanted to show the opposing sides in Sabha that the new Libya had a place for all tribes and ethnic groups.
The Tibu have black skin and some have ties to neighbouring Chad, while their opponents are lighter-skinned ethnic Arabs who see the Tibu as outsiders.
"Every Libyan is important to us. We're going to take care of them like we do take care of any other Libyan, like our brothers and sisters," Keib told Reuters after addressing about 500 local people from the non-Tibu camp.
"This problem has a historical background ... The past regime has used and abused this problem," he said, in reference to Gaddafi's tactic of playing up tribal differences to weaken any opposition against him.
Keib was then heckled by a man who was shouting that the government was late in acting to stop the clashes and called on the military to deal with the Tibu.
Keib tried to talk to the heckler but his security detail ushered him into a car to head onto his next meeting, with Tibu elders.
As his convoy drove through Tibu-controlled neighbourhoods, fighters from the tribe lined the roads, with rifles in their hands. They shouted "Allahu Akbar!" (God is greatest), and smiled and waved at the prime minister's motorcade.
"We need to find a solution for this, I am here for that," the prime minister told the Tibu elders, at a two-hour meeting conducted on mats laid on the ground, after they set out their grievances.
"We do not want the Tibu to be in need, we want things to go well ... It's not Tibu and the rest of Libya. It's all our country," Keib said.
Restoring order in Sabha is not only important internally for Libya but also for stability in the wider region.
In the chaos that followed Gaddafi's fall, the south has been used as a smuggling route for weapons which are reaching al Qaeda in the Sahara and fanning a separatist rebellion by Tuaregs in northern Mali.
Earlier on Sunday, on the journey to Sabha from the airport where he landed, the prime minister's motorcade was accompanied by a heavy security escort, which included vehicles mounted with anti-aircraft guns.
At the entrance to Sabha, militia men from the coastal city of Misrata stood guard. They had been despatched by the government to help restore order. The prime minister was joined in Sabha by Youssef al-Mangoush, chief of the new national army.
There was a separate incident on Sunday that also illustrated Libya's ethnic divisions, in the Mediterranean coast town of Zuwara near the border with Tunisia.
Fighters from the nearby town of Al-Jumail had detained 25 members of the Zuwara local militia, leading to a tense stand-off between the two groups, a representative of the Zuwara council and an Interior Ministry official told Reuters.
"The origin of the problem was that there was a group from Zuwara hunting in the area near Al-Jumail and they shot and killed someone from Al-Jumail by mistake," the Interior Ministry official said.
Zuwara is inhabited mainly by members of the Berber ethnic minority, who fought to overthrow Gaddafi. The town is though surrounded by ethnic Arab settlements, some of which backed Gaddafi in last year's revolt. (Additional reporting by Taha Zargoun in Tripoli; Writing by Christian Lowe; Editing by)