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* Little clarity on how U.N.-mediated deal can be reset

* Angry reaction in Tripoli to idea of Haftar as army leader

* Diplomatic push seen as lopsided and uncoordinated

By Aidan Lewis

TUNIS, May 10 Libyan military commander Khalifa Haftar, a figurehead in the east of the country, and Fayez Seraj, the head of a U.N.-backed government in Tripoli, appeared at ease as they broke more than a year of deadlock between them at talks in Abu Dhabi last week.

The meeting may have been amicable but it is unclear if either man will sway a complex array of factions on both sides of Libya's divide towards compromise.

Also unclear is whether foreign states with divergent strategies in Libya will help them do so -- especially as U.S. President Donald Trump has yet to spell out a policy on Libya.

At stake are the prospects for stabilising and unifying Libya, which splintered into competing fiefdoms after the NATO-backed uprising that toppled Muammar Gaddafi in 2011.

Western powers had hoped Seraj's Government of National Accord (GNA) would play that role. But though oil production has risen and Islamic State was defeated in its stronghold of Sirte under its watch, the GNA has been unable to extend its authority or resolve acute security and economic crises since arriving in Tripoli in March last year.

Haftar, meanwhile, built his power base in the east, spurning the GNA as his self-styled Libyan National Army (LNA) took control of most of Benghazi and oil facilities to the southwest.

As the international community pressed to reset the U.N.-mediated deal that created the GNA, Haftar shunned dialogue, refusing at the last minute to meet Seraj in Cairo in February.

"The fact that they met this time was important," said a senior Western diplomat. "Haftar has moved...he is now sounding more amenable to compromise."

STRONGMAN IMAGE

Last month there was also a meeting in Rome between the heads of two parliaments based in Tripoli and the east, one aligned with the GNA and the other with Haftar. Both are naming delegations to negotiate the details of a deal.

But there are few obvious signs of convergence. A statement from the Haftar camp in Abu Dhabi stressed support for the military, battling terrorism, and "addressing the proliferation of armed formations" mirroring the image Haftar projects as a strongman who can crush extremism and curb militias.

Seraj's statement reflected conditions that could contain Haftar -- placing the military under civilian authority, building a democratic state, and preserving "the principles of the 17 February (2011) revolution".

Haftar is said to want a three-member ruling council that includes himself and Aguila Saleh, head of the eastern parliament, alongside Seraj.

But that would leave out key constituencies represented in Seraj's current leadership council, including southern Libya and the city of Misrata, whose powerful military brigades have been broadly aligned with the GNA and against Haftar.

Some more radical Misrata militias that still back an ousted, Islamist-leaning government, and have recently lost ground in Tripoli, are vehemently anti-Haftar.

But even more moderate armed factions aligned with the GNA in the capital reacted with unease after the Abu Dhabi meeting they saw as unfairly bolstering Haftar's strongman position.

"We have said numerous times no to military rule and Tripoli is a red line, whether for Haftar or anyone else," Hashem Bisher, a prominent commander, wrote on his Facebook page.

The reaction became wider and angrier when Seraj's Foreign Minister Mohamed Siyala made comments on Monday that suggested acceptance of Haftar as the head of a national army.

One brigade said it had shut the foreign ministry, where pictures of Haftar were posted captioned: "No to the war criminal Khalifa Haftar".

The Benghazi Defence Brigades (BDB), which includes fighters who have been battling LNA forces as they push west and south, condemned Siyala's comments and questioned the GNA holding "suspicious conferences and meetings".

Seraj did not travel to Egypt for a follow-up meeting with Haftar originally expected on Thursday.

DISJOINTED DIPLOMACY

Western diplomats say foreign mediation has to be synchronised for a political deal to be reached.

The Abu Dhabi meeting was brokered by Haftar's two most prominent foreign backers, the United Arab Emirates and Egypt. Both share the Haftar camp's distaste for the Muslim Brotherhood and back his military campaign against Islamist militants.

Algeria, which hosted a round of talks this week, and Tunisia, are pushing a more inclusive approach. But diplomacy has been disjointed, in part because of uncertainty over U.S. policy under the Trump administration and a delayed leadership change at the United Nations' Libya mission.

That has left a vacuum that medium-sized players with different approaches have been battling to fill, said Jalel Harchaoui, a geopolitics researcher at Paris 8 University specialising on Libya.

"If the U.S. takes a keen interest in Libya again, they would be the only player that could unify these efforts," he said. (Additional reporting by Ahmed Elumami; Editing by Patrick Markey)

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Way forward for Libya uncertain despite "breakthrough" meeting - Reuters