Libyan Islamist-backed parliament General National Congress (GNC) on Tuesday rejected a United Nations peace proposal to form a unity government for Libya.

"The draft accord given by Bernardino Leon, head of the UN mission to Libya, is not the satisfactory state for us to initial it," Omar Hemidan, spokesman of the GNC, announced the decision in a press conference.

Libya has been witnessing a frayed political process after the 2011 turmoil which toppled its leader Muammar Gaddafi. The country is now juggling two rival parliaments and governments.

According to Libya's transitional plan, the June-elected parliament, the House of Representatives (HOR), has already replaced the former interim General National Congress (GNC).

However, the armed Islamist alliance Libya Dawn, which has achieved a series of military progress since July in western Libya, backed the GNC to resume power and form its own government against the new one.

Since last September, the United Nations Support Mission in Libya (UNSMIL) has been struggling to solve the political jigsaw puzzle in Libya by brokering peace talks, but the endless clashes between different armed groups and lack of genuine desire to reach a political solution made the UN efforts fruitless.

In a landmark move, representatives from Libya's two rival parliaments sat together in formal talks about the draft accord for the first time on June 28 in Morocco.

The Libyan House of Representatives formally accepted last Thursday the UN proposal to end war in Libya, while the GNC decided to continue consultations on the latest UN proposal in Tripoli.