A final decision on the resignation will be delayed until the premier's return and the reasons for his move are revealed, he added, according to Lebanon's National News Agency.
Aoun made the remarks at a meeting on Friday with ambassadors in Beirut, including Saudi Charge d'Affaires Walid al-Bukhari. Media reports said Aoun told the Saudi envoy that the circumstances of Hariri's resignation were "unacceptable."
German Foreign Minister Sigmar Gabriel phoned his Saudi counterpart Adel al-Jubeir to express Berlin's concern about the threat of destabilization in Lebanon.
Gabriel told al-Jubeir that Germany believed the progress made under Hariri's leadership "should not be jeopardized," a foreign office spokeswoman said in Berlin.
Chancellor Angela Merkel's spokesman also called on Saudi Arabia and Iran "not to weaken political stability in Lebanon."
U.N. Secretary-General Antonio Guterres declared the political situation in Lebanon "a matter of great concern," warning that a new conflict in the region "could have devastating consequences."
U.S. Secretary of State Rex Tillerson said Washington supports Hariri and denounces possible external meddling in the country's affairs.
"The United States cautions against any party, within or outside Lebanon, using Lebanon as a venue for proxy conflicts or in any manner contributing to instability in that country," Tillerson said, adding that the US was opposed to "any actions that could threaten that stability."
In Riyadh, Hariri has been meeting with foreign ambassadors since Tuesday. His latest meetings included Italian ambassador Luca Ferrari and Russian ambassador Sergei Kozlov, according to his press office.
In a sign of escalating tensions with Beirut, Saudi Arabia, Kuwait and the United Arab Emirates on Thursday advised their citizens against travelling to Lebanon.
Some nationals from the three Gulf countries were seen Friday leaving Lebanon, an official at Beirut's Rafik Hariri airport said. Tourism is a main source of income for Lebanon, which has felt the economic fallout of the civil war in neighboring Syria.
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