Libyan peace talks are to resume next week as UN envoy Bernardino Leon presses on with efforts to strike a political settlement between the country's rival factions, his office said Thursday.

The next round is to be held on Monday in Geneva, a source at the United Nations Support Mission in Libya (UNSMIL) said.

The mission said Leon "was urging the main parties to redouble their efforts... towards narrowing existing differences and forging a common platform" for a solution to the Libya conflict.

Leon "acknowledges that while some of the parties continue to have reservations about what has been achieved to date, it is important for all parties to continue working on jointly addressing and resolving these concerns within the framework of the dialogue process", it said.

Plunged into chaos after the 2011 overthrow and killing of dictator Moamer Kadhafi, Libya has two parliaments and governments vying for power, as a slew of armed groups battle for control of its oil wealth.

The elected parliament, which is recognised by the international community, initialled a UN draft deal on July 11 aimed at setting up a national unity government and holding fresh elections.

Members of political parties, civil society and local officials also signed the agreement.

But the rival parliament known as the General National Congress (GNC) has refused to endorse the draft deal, saying it was "unsatisfactory" and calling for "modifications".

It was not immediately clear who will attend the Geneva talks and whether a GNC delegation would travel to Switzerland.