Hariri made his announcement after returning to Beirut on Tuesday night for the first time since his Nov 4 shock resignation in a statement broadcast from Saudi Arabia.
He said all Lebanese parties must commit to keeping Lebanon out of regional conflicts, a reference to the powerful, Iran-backed group Hezbollah whose regional role is a source of deep concern in Saudi Arabia.
Hariri, back in Beirut, attends national day parade
He said hoped his decision would open "a new gateway for a responsible dialogue".
"I presented today my resignation to President Aoun and he urged me to wait before offering it and to hold onto it for more dialogue about its reasons and political background, and I showed responsiveness," Hariri said in a televised statement.
Hariri's resignation pitched Lebanon to the forefront of the regional tussle between Sunni Muslim Saudi Arabia and Iran, which backs the powerful Lebanese group Hezbollah.
Lebanon army chief calls for readiness at Israel border
Lebanese state officials and senior politicians close to Hariri say Riyadh forced him to quit and held him in the kingdom, which Saudi Arabia and Hariri have denied.
The resignation took even Hariri's aides by surprise. Hariri's return to Lebanon followed an intervention by France. A long-time Saudi ally, Hariri cited fear of assassination in his resignation speech, and attacked Iran and its powerful Lebanese ally Hezbollah for sowing strife in the Arab world.
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