President Emmanuel Macron has invited Lebanon's Saad al-Hariri and his family to France, the French presidency said in a statement.
The EU's diplomatic chief Federica Mogherini said Tuesday she expected Lebanon's prime minister to return to the country "in the coming days" following his sudden resignation.
Earlier in the day, Hariri, who has remained in Saudi Arabia since his abrupt resignation on November 4, tweeted that he was "fine", adding he planned to return to Lebanon.
In his sharply worded resignation from Saudi Arabia, Hariri, 47, accused Iran and its Lebanese ally Hezbollah of destabilising his country and the broader region. He said Hariri needed to return to Lebanon to prove he was free.
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.
France, Lebanon's onetime colonial ruler, has been trying to mediate in the crisis between Lebanon and Saudi Arabia.
He added that the Lebanese state could not wait long for Mr Hariri's return.
Aoun, 82, has yet to formally accept Hariri's resignation and has said he will not do so before meeting him in person in Lebanon.
In his first public statement, Bahaa Hariri blasted Iran and its militant Lebanese proxy.
However, Riyadh's Western allies have struck a tone different from that of Saudi Arabia, appearing to throw their weight behind both Hariri and the Lebanese state, whose army is a major recipient of US aid.
On his Twitter account Tuesday, Hariri wrote in Arabic that he was "a thousand good" and planned to return to Lebanon in two days "God willing". Saudi Arabia is seeking to impose its will on the Lebanese government.
"After speaking with Saudi Crown Prince Mohammed bin Salman and the Lebanese Prime Minister Saad al-Hariri the president has invited Saad al-Hariri and his family to France", the Elysee said.
However, Nasrallah has also said that he would not comment on Hariri's speech that he gave to announce his resignation because he saw it as a "Saudi statement".
Saudi al-Arabiya television quoted him as saying he supported the reasons for Hariri's resignation.