U.N.-sponsored talks in Geneva between rival Libyan factions aim to reach a political settlement to form a unity government that a majority of Libyans can support.

U.N.-sponsored talks in Geneva between rival Libyan factions aim to reach a political settlement to form a unity government that a majority of Libyans can support, U.N. Special Envoy for Libya Bernadino Leon said on Wednesday, and he hoped armed factions would observe a cease-fire to support the process.

Part of the Tripoli faction will only decide on Sunday whether to join the talks, but Leon said the door would stay open and he was encouraged that several municipalities allied to Tripoli had decided to come

Western governments hope talks in Geneva this week would ease a crisis in Libya where two rival governments and their forces are vying for control, three years after the fall of Muammar Gaddafi.

"The United Nations Support Mission in Libya (UNSMIL) has confirmed that the meeting of Libyan parties will start tomorrow Wednesday 14 January 2015 in the afternoon at the Palais des Nations in Geneva," a U.N. statement said.

Bernardino Leon, Special Representative of the Secretary-General for Libya and Head of UNSMIL, will give a press conference before talks start, it said, adding that the list of participants would follow.

The internationally recognized government of Prime Minister Abdullah al-Thinni has been based out of eastern Libya since the summer after a faction called Libya Dawn took over Tripoli and set up its self-declared government and legislature.

Tripoli-based forces said their legislature had postponed a decision over joining the Geneva talks until Sunday because of concerns about how the negotiations were organized.

"We do not reject dialogue, but we believe that the UN rushed to determine the date of the dialogue and its mechanisms," said Omar Hmaidan, spokesman for the Tripoli legislature on Monday. "We have decided to postpone the vote to participate or not to next Sunday."

The decision from Tripoli appeared to push back the chance of any meaningful talks between the two sides.

A delegation from the elected House of Representatives, representing Thinni's government, was already in Tunisia waiting to fly to Geneva, according to a parliament representative.