Aqila Salah, who heads the internationally recognised parliament sitting in the east, met Nuri Abu Sahmein of the Tripoli-based General National Congress, the report said.
The Annaba channel showed the two men meeting in Malta in the presence of representatives of both chambers ahead of the expected signing of the agreement in Morocco Thursday.
It followed a gathering in Rome of a US- and Italian-led group of world powers and regional players that urged Libya's warring factions Sunday to lay down their arms and back the new unity government.
In Rome, US Secretary of State John Kerry dismissed criticism that the proposed government was being imposed from outside in the absence of consensus on the ground.
The security situation also makes it uncertain that the new administration will be able to base itself in the capital.
Kerry insisted that majorities of both parliaments supported the peace plan and that only fringe players were obstructing progress.
Libya has had rival administrations since August 2014, when the Islamist-backed Fajr Libya militia alliance overran Tripoli, forcing the elected government to take refuge in the far east near the border with Egypt.
The deal had initially been due to be signed in Skhirat, Morocco tomorrow, but a Moroccan diplomat told AFP the ceremony would now take place the following day at 1100 GMT.
A spokesman for the UN mission to Libya said the postponement was for logistical reasons relating to the delegations' travel to Morocco.
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