Years of political turmoil since the 2011 overthrow of long-time dictator Moamer Kadhafi have left Libya divided between rival governments and beset by violence as militia forces battle for power.
The UN-backed Government of National Accord (GNA), based in Tripoli since March 2016, has struggled to impose its authority across the country, particularly in the far east, dominated by military strongman Khalifa Haftar who supports a rival parliament.
On Monday night, the head of the delegation representing the parliament based in the east, Abdessalem Nssya, accused the rival authorities of backtracking on several points.
Nssya said his team was suspending its participation in the talks which have been under way in Tunis since September 26, after UN envoy Ghassan Salame presented a plan to end the chaos in Libya.
Representatives of the rival Libyan authorities have already held two rounds of talks in Tunisia aimed at amending a UN-backed political agreement struck in 2015.
The deal had led to the creation of the GNA, a unity government headed by Prime Minister Fayez al-Sarraj.
During the first round of talks in September, rival Libyan politicians had agreed to set up a three-member Presidency Council and a new government.
Disagreement centres on an article of the 2015 deal which gives the GNA the power to name the head of the armed forces.
A second round of talks was held this week and reached a “pivotal” point “when both sides came close to a clearer understanding of the selection-mechanism for the Presidency Council”, the United Nations Support Mission in Libya (UNSMIL) said in a statement.
UNSMIL said the meeting was later adjourned to allow for “internal consultations” to take place on Tuesday, noting that “much work remains ahead” but without specifying when the talks will resume.
Salame presented a roadmap to the United Nations on September 20, proposing that a new constitution be put before a referendum, paving the way for elections in Libya.