The new decision came hours after the premier landed back in Lebanon for the first time since announcing his resignation in a statement from Saudi Arabia on November 4.
"I discussed my resignation with the president of the republic who asked me to wait before submitting it... and allow for more consultations," Hariri told reporters after meeting Aoun.
"I agreed to this request."
Lebanon has been gripped by the political crisis precipitated by Hariri's resignation, including the question of whether the premier was being detained in Saudi Arabia, where he remained for two weeks after stepping down.
Hariri holds dual Saudi-Lebanese citizenship, and denied he was being held against his will by Riyadh, a close political ally, but accepted a French invitation to visit Paris, leaving the kingdom on November 18.
After stops in Egypt and Cyprus yesterday, he landed in Beirut close to midnight, and today appeared at the country's Independence Day celebrations marking 74 years since the end of France's mandate in Lebanon.
He appeared relaxed, at times smiling and appearing to joke with those alongside him during the military parade to mark the national holiday.
He also harshly criticised Saudi Arabia's arch-rival Iran, and its Lebanese ally Hezbollah, saying they had taken over Lebanon and destabilised the region.
The resignation of the Sunni leader was seen as raising the temperature in a long-running rivalry between Saudi Arabia and Iran that has played out across the region.
In Lebanon, the political scene is deeply divided between Hariri's Saudi-backed bloc, and that led by the powerful Shiite Hezbollah group, which is backed by Iran.
He had already signalled that he could consider rescinding his resignation altogether if Hezbollah pledged to respect Lebanon's policy of "disassociation" from regional conflicts.
Hariri and his allies say the group, with Iranian support, has violated this policy by fighting in neighbouring Syria in support of President Bashar al-Assad's government, as well as providing assistance to Huthi rebels battling Saudi Arabia in Yemen.
Hezbollah's chief Hassan Nasrallah has said the group still considers Hariri the country's prime minister and suggested it was open to talks, though whether any real compromise could be reached remained unclear.
If no deal is reached and Hariri's resignation stands, Aoun has two options -- rename him premier or choose another prominent Sunni figure to lead a new cabinet.
Under Lebanon's power-sharing arrangement, the country's top political posts are reserved for different sects, with the presidency set aside for a Maronite Christian, the prime minister's office for a Sunni Muslim, and the parliament speaker for a Shiite Muslim.
Hariri's resignation comes less than a year after he took office, as part of a deal with Aoun, whose party belongs to the bloc led by Hezbollah.
His first term as prime minister ended abruptly.
In January 2011, as he was meeting then-US president Barack Obama in Washington, Hezbollah and its allies withdrew their ministers and brought down Hariri's government.
Hariri's resignation has been seen as part of a broader pattern of escalating tension between Iran and Saudi Arabia.
On the day he resigned, the kingdom said it intercepted a ballistic missile fired at Riyadh airport by Shiite rebels in Yemen.
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