The Libyan National Army has announced a ceasefire conditional on the other party committing to it, according to a spokesperson.
The announcement of a ceasefire came hours after German Chancellor Angela Merkel said Libyan peace talks will be held in Berlin, as Turkey and Russia appealed to the north African nation's warring factions to enter a ceasefire.
The LNA in April launched an offensive against the capital, seat of the UN-recognized GNA.
Since a 2011 NATO-backed uprising that killed longstanding dictator Muammar Qaddafi, Libya has been plunged into chaos.
The LNA led by Khalifa Haftar launched an offensive to capture the Libyan capital of Tripoli in April vowing to end the rule of militias that include hardline groups linked to al-Qaeda and others.
General Haftar has reportedly received support from international allies opposed to extremism and the Muslim Brotherhood.