PARIS, May 20 (Reuters) - It would be "unthinkable" for eastern Libyan forces to join a U.N.-backed unity government until militias aligned to it have been disbanded, General Khalifa Haftar, who heads up troops in the east, said in an interview broadcast on Friday.

A December unity deal was meant to end the divide between rival governments in the capital Tripoli and the east who have vied for control over the country and its oil resources since 2014, backed by competing factions, who helped oust Muammar Gaddafi five years ago.

But in an ominous early sign of a possible new showdown, eastern and western factions have sent separate armoured columns towards Gaddafi's home town Sirte, now in the hands of fighters from Islamic State.

Western powers see Fayaz Seraj, the head of the Government of National Accord (GNA), as the best hope of unifying political and armed factions to take on Islamic State. The government arrived in Tripoli in late March and is still trying to establish its authority.

He urged the east last week to join a unified military command centre to coordinate efforts against Islamic State and asked major powers to ease a United Nations Security Council arms embargo for his administration.

"Firstly, We have no links with Mr Seraj and the Presidential Council which he leads is not recognised by the parliament (in the east)," Haftar told i-Tele news channel in an interview in Libya.

"Secondly, on this unified command centre, I would like to stress that Mr Seraj relies on militia and we refuse them. An army cannot unify with militias so they must be dismantled. It's unthinkable to work with these armed factions."

Haftar leads the Libyan National Army (LNA), but his role in any national military force as a possible defence minister or army chief has become one of the most divisive problems in unifying the two sides.

For two years Haftar has been waging a campaign, primarily in Benghazi, the biggest city of the east, against Islamist militants and other former rebels who view him as an Egyptian-backed relic of the old regime with presidential ambitions.

"Daesh does not have the capacity to face the Libyan armed forces, but the battle could take time," Haftar said, using the Arabic acronym for Islamic State.

"If the international community supports us, and I ask it to do so by lifting the embargo on weapons, then we could eliminate Daesh in Libya definitively and quickly," he said.

Islamic State gained control over Sirte last year and has built up its most important base outside Syria and Iraq in the Libyan coastal city. However, it has struggled to hold on to territory elsewhere in Libya.

(Reporting By John Irish; editing by Ralph Boulton) ((john.irish@thomsonreuters.com; 0033-1 49 49 53 42; Reuters Messaging: john.irish.thomsonreuters.com@reuters.net))