The country has in recent months been hit by deadly attacks on military and police officers in the east and strikes at its main oil terminals, in some of the worst unrest since dictator Moamer Kadhafi was toppled in October 2011.
"It is a question of forming a commission made up of Libyan personalities from civil society who will initiate a debate around the issues of the future constitution, national reconciliation, displaced persons, disarmament or security," Zeidan said.
"This commission that will oversee this dialogue will be entirely independent from the government and from the General National Congress (the highest political authority in the country)," Zeidan said at a joint press conference with former vice-president Jumaa Attiga and UNSMIL chief Tarek Mitri.
Mitri said the campaign would help "highlight the diversity of Libyan society," adding that the UN was ready to lend its "support, its experience and technical knowledge to this initiative".
The initiative comes against a backdrop of rising instability in Libya, with tension in the west of the country, where members of the Wershifana tribe clashed with residents of the town of Zawiya.
In the east, oil terminals in eastern Libya have also been hit by strikes since the end of July.