Libya's internationally recognised parliament is expected to hold a vote of confidence Tuesday on a UN-backed national unity government for the conflict-ridden North African nation, a lawmaker said.

Deputy Aisha al-Aquri said the legislature wrapped up debate Monday on the line-up proposed by a presidential council and would meet again on Tuesday "to approve the national unity government".

Oil-rich Libya has had rival administrations since the summer of 2014 when the recognised government fled Tripoli after a militia alliance including Islamists overran the capital.

That alliance has established its own administration and parliament called the General National Congress, while the internationally recognised legislature is based in the eastern city of Tobruk.

The United Nations has been pushing both sides to back a unity government.

The Presidential Council, born of an agreement in December under UN auspices between representatives of the rival parliaments, proposed last week the formation of a unity government of 18 members.

Parliament has been meeting since Saturday to discuss the line-up submitted by prime minister designate Fayez al-Sarraj.

UN envoy Martin Kobler travelled Sunday to Tobruk saying he wanted to "help" with the vote of confidence but "not to interfere".

Libya has been torn by strife since Muammar Gaddhafi was overthrown and killed in 2011 following a rebellion supported by Western military intervention.

The chaos that has reigned since has allowed the jihadist Islamic State group to establish a foothold, and IS group now controls the coastal city of Sirte and its surroundings.