Bahaa Hariri, in a statement to the Associated Press, said he supported his brother's resignation and thanked Saudi Arabia for "decades of support" for Lebanon's institutions.
The Lebanese president has publicly acknowledged that Prime Minister Saad Hariri is being detained in Saudi Arabia along with his family, calling it "an act of aggression" against Lebanon.
Writing on Twitter, Aoun said Hariri's detention represents a breach of human rights and Lebanon can not wait a long time for his return as the state must continue to operate.
Bahaa Hariri, right, and Saad Hariri visit the scene on February 19, 2005, where their father Rafik, the prime minister, was assassinated in Beirut.
Aoun has called the alleged detention of Saad Hariri a breach of human rights, emphasizing that nothing justifies the former prime minister's return to Lebanon.
Aoun said the Saudis were also holding family members of Hariri, adding: "We have not previously asked for their return, but we have confirmed that [his family] is also detained and family members are being searched as they enter and leave the house." .
The EU's diplomatic chief Federica Mogherini said Tuesday that European diplomats had "close contacts" with Hariri and also expected him to return home "in the coming days".
"I want to reiterate that I am very, very well and I will return if God wills it to the beloved Lebanon just as I promised. You'll see", he wrote.
On Tuesday, he announced his return in two days, after a meeting in Riyadh with the Maronite Patriarch Bechara Rai.
Hariri warned on Sunday in his first interview since resigning of possible Gulf Arab sanctions against Lebanon and of the risk to the livelihoods of the 300,000-400,000 Lebanese in the Gulf.
He added: "It is not possible to decide on a resignation submitted from overseas, so go back to Lebanon to submit his resignation or to refer to it or to discuss its reasons and ways to deal with it".
After Hariri's resignation, Saudi Arabia accused the Lebanese government of declaring war on it because of Hezbollah's pivotal role in Lebanese politics.
In his statement, Hariri said he was stepping down because he feared the growing influence of Iran on Lebanon's government. He has yet to return to Lebanon from Riyadh, which had always been considered his chief political patron.
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