The Libyan National Congress, considered the rebel government in Tripoli, has conditionally approved the fourth draft of a peace agreement with the Tobruk-based internationally-recognized government, Efe news agency reported.
The draft was presented by UN's special envoy to Libya, Bernardino Leon, who was hopeful of a breakthrough.
"The draft has some positive points but needs some modifications too. The amendments will be presented to the head of the United Nations mission," National Congress spokesman Omar Humaidan told reporters on Tuesday.
"The best way to resolve (the conflict) is to accept this draft and bring the country out of the crisis," he added.
The proposal, presented by the Spanish diplomat a few days ago to end months of fruitless efforts, is being studied by the government in Tobruk too.
The media says there is a lack of consensus in Tobruk.
The so-called "House of Representatives" is divided into those who support the proposal, those who wish to introduce amendments and those who completely reject it on the ground it conceded too much political representation to a government (in Tripoli) that should have been dissolved after last year's elections.
Libya has been a failed state since 2011 when rebels, backed by the international community, overthrew the dictatorial regime of Muammar Gaddafi.
Following recent elections, two governments emerged in Libya: an Islamist one in Tripoli and another with more international credibility, in Tobruk.
Both governments are backed by different Islamist militant groups, warlords and tribal leaders.
In recent months, the Libyan wing of the Islamic State (IS) terrorist group has taken advantage of the conflict in the country to consolidate its position in the city of Dema and advance towards the coastal city of Sirte, located 435 km from Tripoli, which it claims to have captured.
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