Senior commanders meet in capital Tripoli in unprecedented talks, with both sides agreeing to name a single chief and begin reunification of army split since 2011 civil war in the North African country.
A group of protesters said it would occupy city streets and squares until all the ruling political bodies "announce their resignation in public".
Libyan legislative leaders have quit talks in Geneva on a constitution and elections without reaching a deal, pausing diplomacy to resolve a standoff that has imperilled a two-year peace process.
UN special adviser on Libya Stephanie Williams urged Libyan officials to convene within 10 days to bridge the gaps between the two sides.
The talks come after clashes broke out in Tripoli between rival groups, raising fears of escalating violence in the conflict-hit country.
Stephanie Williams meets UN-recognised PM Abdul Hamid Dbeibah and Fathi Bashagha, named by eastern-based rival parliament to head a new government, as political chaos reigns in the North African country.
Nothing is certain and everything is debatable in Libya following the postponement of elections.
Libyan delegates chose a list of candidates in a UN-hosted process aimed to give balance to regional powers and various political and economic interests.
The top UN official for Libya said that an advisory committee for representatives of Libya's different regions has proposed a way forward for choosing a transitional government that would lead the war-torn country to elections late this year.
A change in the UN’s approach and strategy is needed, not its personnel.
UN envoy for Libya Stephanie Williams heads online meeting of Libyan Political Dialogue Forum a week after talks in Tunisia failed to name an executive authority.
"Ten years of conflict cannot be resolved in one week," said acting UN envoy Stephanie Williams as delegates decide to resume talks online next week to discuss a reformed structure and role for the executive authority.
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