Hariri resigned on November 4 from Saudi Arabia, throwing his coalition government and the country into crisis, but rescinded the move after returning home, to allow time for negotiations.
He has demanded that his coalition ally, the Lebanese militant Hezbollah group, remove itself from regional conflicts, from Syria to Iraq and Yemen. Hezbollah denies playing a military role in Yemen but has fighters in both Iraq and Syria.
Aoun separately met today with several officials including the head of Hezbollah's parliamentary bloc, Mohammed Raad, who later told reporters they discussed "reactivating" the government.
Christian leader Samir Geagea, a harsh critic of Hezbollah, told reporters after meeting Aoun that his group will not resign from the government.
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"Disassociation should be in action and not through words, this means actively withdrawing from the region's conflict," he said, referring to Hezbollah.
Saudi Arabia and Iran are fighting proxy wars in the region and the conflict has affected Lebanon over the past years.
Hariri's resignation came amid mounting tensions between Saudi Arabia and Iran. Saudi Arabia has accused Hezbollah of declaring war on the kingdom by supporting Yemen's Houthi rebels, who fired a ballistic missile the night of Hariri's resignation that was intercepted near Riyadh.