The call for elections was made in a joint statement at the end of two days of closed-door talks attended by representatives of 13 leading political parties.
Hariri's decision came after arrival back in Lebanon for the first time since resignation announcement in a statement from Saudi Arabia on November 4.
UN Security Council's Resolution 242 was agreed unanimously on November 22, 1967, five months after a crushing Israeli offensive during which it occupied vast swathes of Arab territory.
Saad Hariri is expected to attend Lebanon's independence day parade in the capital Wednesday before meeting with President Michel Aoun, who has said he would not accept Hariri's resignation until he received it in person.
The UN Security Council unanimously approved a resolution urging tougher action to crack down on human trafficking worldwide just days after a video showed young men being auctioned off as slaves in Libya.
Egytian President Abdel Fattah el Sisi hosts Saad Hariri at the presidential palace in Cairo and the two leaders discuss the latest developments in Lebanon and the region. Hariri departed back for Lebanon after the meeting.
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