Aoun, the leader of the Free Patriotic Movement and a former president, said he refused an invitation to dine with Hariri, blaming him for waging a media campaign against the opposition lawmaker, Lebanon's Daily Star newspaper reports.
"How can I possibly accept the invitation of someone who has been personally attacking me and insulting me in the media?" he asked.
Aoun further complained Hariri and his March 14 coalition did not see his party fit to take part in the next Cabinet, blaming Lebanese political groups for having a "mafia attitude."
March 14 lawmakers are reportedly upset over Aoun's insistence, along with Hezbollah, that his son-in-law and caretaker Telecommunications Minister Jebran Bassil retain his position despite losing in the June parliamentary elections.
Hariri secured a victory for his March 14 alliance in the June elections over the March 8 opposition movement.
Lawmakers had agreed to a power-sharing agreement in the next government, allocating 15 seats to March 14, 10 to March 8 and five for allies of Lebanese President Michel Suleiman.
That formula was disrupted when Druze leader Walid Jumblatt abruptly left March 14 recently, saying his "necessary" alliance with the Western-backed alliance had ended.