Libyan National Army forces will withdraw 2-3 kilometres from all front lines in Tripoli by midday on Wednesday.
A spokesman for the group, led by Field Marshal Khalifa Haftar, said the pull-back was to allow residents to move more freely during the Eid Al Fitr holiday to mark the end of Ramadan that is expected to begin over the weekend.
Ahmed Al Mismari called on the LNA's opponent, the Government of National Accord (GNA), to do the same but did not say whether its own withdrawal was contingent on it doing so. The GNA has not commented yet.
In its biggest advance in a year, the GNA on Monday captured Watiya airbase, an important LNA stronghold and its only major airbase near Tripoli, along with an abandoned Russian-made Pantsir air defence system.
The LNA said they abandoned the base as part of a planned strategic move and the only weapons taken were old and obsolete.
UN special envoy to Libya Stephanie Williams told the Security Council on Tuesday night that the capture of the air base risks turning the conflict into a pure proxy war given the significant Turkish support to GNA forces in the fight.
"The control of this strategic airbase may trigger further escalation, turning the Libyan conflict into a pure proxy war," she said.
On Tuesday, the GNA took the towns of Badr and Tiji in western Libya as the LNA said it had moved out of some positions around Tripoli, where the front lines have been mostly static for nearly a year.
Ms Williams urged the Security Council to pressure foreign actors to stop helping the warring parties there, warning the flood of arms and fighters into Libya would only intensify fighting.
UAE's Minister of State for Foreign Affairs Dr Anwar Gargash said his country's position on the crisis was "firm and clear", that the "only acceptable path forward involves an immediate, comprehensive ceasefire and return to the political process".
"This crisis has been going for almost ten years," he said on Twitter. "Libyans will not have the chance to create a stable or prosperous country until combatants aim higher than tactical territorial gains. These are mirages of victory and no substitute for a political process."