* Prime minister seized at dawn by gunmen, held for six hours
* Former rebels blame Zeidan for U.S. capture of al Qaeda suspect
* Libya's government struggles to contain rival militias
By Ghaith Shennib and Ulf Laessing
TRIPOLI, Oct 10 (Reuters) - Libyan gunmen on the government payroll seized the prime minister in his nightshirt on Thursday and held him for several hours, in a new manifestation of the anarchy that has followed the overthrow of Muammar Gaddafi.
The militia justified its bloodless dawn raid on the luxury hotel where Ali Zeidan lives under notionally tight security by saying he should be investigated for aiding U.S. forces in their capture in Tripoli on Saturday of a Libyan al Qaeda suspect.
But the liberal former diplomat has no shortage of critics among Islamist and other leaders for his failure to resolve strikes that have paralysed oil exports or to impose order since he was elected premier a year ago by the interim legislature.
A morning of negotiations while Zeidan was held at an Interior Ministry office by a group employed by the state to provide security in Tripoli ended with him being freed unharmed and then pointedly avoiding criticism of his erstwhile captors.
He called for "wisdom" and national unity and praised former anti-Gaddafi rebel groups for helping secure his release. Underlining the sense of chaos generated by such forces, still under arms two years after Gaddafi fell, members of the militia which seized Zeidan tried to deny their group's involvement.
"His kidnapping clearly indicates that his government is not cohesive, and that not only is his government not in control of the country, but that he is not in control of his government," said Geoff Porter of North Africa Risk consulting.
World oil prices rose more than 1 percent on speculation that Libyan crude experts would not quickly return to normal after weeks of disruption. Able to supply about 2 percent of world demand, and also a big supplier of gas to Europe, Libya's six million people can look forward to considerable prosperity, but rivalries over control of resources has hampered investment.
The killing 13 months ago of the U.S. ambassador during an Islamist attack on Washington's consulate in Benghazi drew world attention to Libya's problems. But daily confrontations, including sieges in recent months of government ministries and oil installations, have posed greater problems for its rulers.
U.S. Secretary of State John Kerry said Zeidan's abduction showed the need to built the capacity of the Libyan state, whose formal armed forces, made up of ex-Gaddafi troops and some of his enemies, have proven no match for mobile squads of gunmen riding pickup trucks bristling with heavy weaponry.
In France, which took a lead in backing the 2011 uprising, President Francois Hollande said: "We already had great concerns about the situation in Libya and what happened to the prime minister has reinforced those worries."
Hollande sent French troops into Mali early this year to confront an Islamist revolt in its former colony that was fed by arms and fighters from Libya. He said on Thursday Paris was ready to increase cooperation with the Libyan authorities to prevent it being a haven for militants. "We must be there to cooperate with Libya to put an end to these groups," he said.
British Prime Minister David Cameron said he had called Zeidan to offer further support to stabilise Libya.
Libyans, especially from the restive east, far from Tripoli, formed a significant component of al Qaeda and other fighters while Gaddafi was in power. Some benefited from asylum in the West as opponents of Gaddafi. Some, too, were sent back to face torture in his jails after he made peace with the West.
The fall of the veteran ruler, who was killed in fighting on Oct. 20, 2011, encouraged some radical Islamists to return home, while others emerged from prison.
Some of these are now cooperating with other groups in Africa, worrying Western powers who see an increasing Islamist threat, from Nigeria in the West, through the Sahara desert, to the likes of Somalia's al Shabaab in the east - the group behind a bloody attack on a shopping mall in Kenya last month.
The incident, which follows days of Islamist anger at the U.S. raid which snatched al Qaeda suspect Abu Anas al-Liby, also highlighted the dilemmas facing Libya's government in relations with the United States and other Western powers which provided the air power that helped them end Gaddafi's 42-year rule.
Zeidan, who lived in exile in Geneva after defecting from Gaddafi's diplomatic service three decades ago, had expressed surprise and annoyance about the U.S. operation - distancing himself as Islamists vowed reprisals against U.S. interests.
But that failed to convince his critics, who said they took Zeidan into custody because Kerry had said the Libya government had been informed of the mission which seized Liby outside his house and flew him to a U.S. warship for questioning.
Zeidan made no mention of the issue after his release.
The group which bustled him from the seafront Corinthia Hotel, a heavily guarded complex housing diplomats and senior government officials, was the Operations Room of Libya's Revolutionaries, which has criticised Zeidan in recent weeks.
Though photographs circulating on social media showed Zeidan apparently at ease with his smiling captors on Thursday, the Operations Room's spokesman, Abdulhakim Belazzi, had last week launched a bitter tirade about the prime minister on television.
"What have you done for Libya?" he shouted. "You took control at a time when Libya was moving forward and developing.
"Now you've destroyed everything."
A visit by Zeidan last week to neighbouring Egypt, where the Muslim Brotherhood government was ousted by the army in July, also angered Libyan Islamists who accused the prime minister of endorsing the overthrow of President Mohamed Mursi.
Zeidan was among those who persuaded French and British leaders to support the 2011 revolt against Gaddafi. Last month, on a visit to London, he appealed for more Western support to rein in the former rebels.
After the Arab Spring revolts that ousted several autocratic leaders, Libya's transition has been one of the messiest.
It still has no new constitution, Zeidan faces a possible vote of no confidence and its transitional assembly, the General National Congress, is paralysed by divisions between the secular National Forces Alliance and the Muslim Brotherhood.
"Is this a wake up call?" asked one Western diplomat. "Will it frighten the political class into understanding that they can't carry on squabbling and that they have to work together?"