"Nothing justifies the failure of Prime Minister Saad Hariri to return for 12 days, therefore we consider him to be held and detained, contrary to the Vienna Convention", Aoun said in a tweet on the official Lebanese presidency account.
Lebanon has accused Saudi Arabia of detaining Hariri since his surprise resignation, announced from Riyadh on November 4, which plunged his country into political crisis.
The head of Future TV, affiliated with Hariri's party, says the prime minister is expected back before Sunday, when Arab foreign ministers meet in Cairo in an emergency session at Saudi Arabia's urging.
Lebanese President Michel Aoun this week accused Saudi authorities of "detaining" the premier.
"He will come to France and the prince has been informed", Le Drian told reporters, referring to powerful Saudi Crown Prince Mohammed Bin Salman with whom he held talks the night before.
El-Rai told reporters at Beirut's worldwide airport that Hariri's return would restore normalcy in Lebanon.
Hariri's office said he met several diplomats in Riyadh on Monday including the British and German ambassadors. According to the New York Times, Nasrallah said, "We, Hezbollah, did not wish for this". Iran supports Hariri's main rival in Lebanon, Hezbollah, which is also a partner in Hariri's unity government.
Aoun is an ally of Hezbollah but had been close to Hariri before the crisis.
Hezbollah, a group of Iran-backed Shiite Muslims centered in Lebanon, is the dominant political and military force in Lebanon.
An official in President Emmanuel Macron's office said Hariri is expected in France in the coming days.
In parallel, Maronite Patriarch Beshara al-Rahi's visit to Riyadh and his stances were welcomed by Lebanese political parties, except for Aoun's Free Patriotic Movement, whose member, Mario Aoun, described Rahi's recent positions as "politically inconvenient in the circumstances we are living today".
A source claims that Hariri will accept the invitation and will take his family with him, who are now in Saudi Arabia as well.
On Monday, French Foreign Minister Jean-Yves Le Drian said "we are preoccupied by the situation in Lebanon".
Le Drian raised concern over Iran's role in the region. Hariri's government is a power-sharing coalition that includes Hezbollah, but Riyadh has made clear it opposes the group's influence. His father, former Prime Minister Rafik Hariri, was killed in a 2005 bombing. "He leaves when he wants to", he said.