CAIRO- Libya's rival central bank branches said they had taken a big step towards reunifying on Thursday as part of a U.N.-backed peace push between warring factions in east and west.

The Central Bank of Libya (CBL) split when the country divided in 2014, but the rival branches have made progress over the past year towards fully reunifying, a major goal of international peace plans.

Tripoli-based CBL Governor Sadiq al-Kabir and the head of the eastern CBL branch, Ali Salim al-Hibri, signed an agreement on a four-stage plan for reunification including the appointment of an external consultant, the CBL said in a statement. The eastern CBL's information office said the two sides had unified their boards of directors and work on technical committees had begun.

Last month Kabir told Reuters after a meeting with Hibri that he hoped the first stage of unification could be accomplished by July.

Economic divisions have added to the oil exporting country's chaos and led to differing exchange rates, liquidity shortages and ballooning public debts that further hurt Libya's battered economy.

However, efforts to resolve political divisions in Libya remain fragile with the fate of an interim unity government in doubt as negotiations among factions and leaders continue following last month's failed attempt to hold an election.

(Reporting by Ayman al-Warfali in Benghazi, Lilian Wagdy in Cairo and Angus McDowall Editing by Raissa Kasolowsky and Andrew Heavens)