(Reuters) -- Libya’s factions have agreed to a new round of United Nations-backed negotiations to attempt to end the conflict destabilizing the North African country three years after Moammar Gadhafi was toppled in a civil war. The meeting, announced after U.N. envoy Bernardino Leon met rival parties in Libya, will take place in Geneva next week, the U.N. mission said in a statement Saturday.

Libya has slipped deeper into division since the August 2011 overthrow of Gadhafi, with two opposing governments and two parliaments, each backed by competing groups of heavily armed former rebel fighters.

“In order to create a conducive environment for the dialogue, Special Representative Leon has proposed to the parties to the conflict a freeze in military operations for a few days,” the U.N. said. Its statement did not make clear who would attend the talks or give an exact date. But it said the meeting would seek to address the formation of a unity government, drafting a new constitution and ending of hostilities.

Abdulqader Hwaili, a member of the parliament in Tripoli, told Reuters the Geneva talks would not be direct. But they would include members of the rival Tripoli parliament and elected House of Representatives, as well as members of the two armed forces, Libya Dawn and Operation Dignity.

“The talks in Geneva will be indirect because the two sides do not recognize each other,” he said. “If there will be [a] chance to hold direct talks, that will depend on the first round.”

Negotiators have struggled to bring the two sides to the table during months of consultations because of their competing demands. Fighting has also complicated attempts to broker talks.

“This represents a last chance, which must be seized. Libya is at a crucial juncture; the different actors should be in no doubt of the gravity of the situation that the country finds itself in,” European Union foreign-policy chief Federica Mogherini said in a statement backing the talks.

After weeks of fighting in the summer, an armed faction, Libya Dawn, allied to the western city of Misrata, took over Tripoli, driving out fighters from the city of Zintan who had set up in the capital after the fall of Gadhafi.

Libya’s internationally recognized government of Prime Minister Abdullah al-Thinni and the elected parliament now operate out of the east. Most countries pulled their diplomats out of Tripoli after the city fell to Libya Dawn forces.

Each faction claims the mantle of true liberators of Libya, each brands its fighters the real army, and each seeks international recognition in a conflict that Western powers and African neighbors worry will fracture Libya.

(Reporting by Tripoli staff; writing by Patrick Markey, editing by Crispian Balmer and Dominic Evans)