Hezbollah's involvement in regional conflicts poses a threat to the security of Lebanon and is a destabilising influence in the Middle East, US Secretary of State Rex Tillerson said on Thursday.
The row has worsened a standoff between Berri, a Shia, and Aoun, a Maronite Christian, that threatens to ignite sectarian tensions in the run-up to a parliamentary election in May.
The leader of Lebanon's Hezbollah on Friday accused Israel of a bomb attack that wounded a member of the Palestinian group Hamas in the Lebanese city of Sidon, calling it an act of aggression.
Israeli jets and ground-to-ground missiles struck Syria early on Tuesday, Syria's army said, as Israeli Prime Minister Benjamin Netanyahu reiterated he would do what was needed to stop Hezbollah gaining "game-changing" Iranian weapons.
Walid Jumblatt also condemned Iranian "dictates", an apparent response to a statement by the commander of the Iranian Revolutionary Guards this week that disarming of the Hezbollah was out of the question.
The Arab League held an extraordinary general meeting on Sunday in Cairo at the request of Saudi Arabia, which called the ministerial-level session to discuss "violations" by its rival Iran.
Hariri has since Saturday been in Paris, where he met French President Emmanuel Macron, and has said he will return to Lebanon by Wednesday for its Independence Day celebrations.
Lebanese President Michel Aoun said earlier this week that Hariri, who abruptly announced his resignation while in Saudi Arabia on November 4, was being held hostage by Riyadh.
Adel al-Jubeir said Saudi Arabia was consulting its allies about what leverage to use against Lebanese militant group Hezbollah to end its dominance in the small Mediterranean nation and intervention in other countries.
Saad Hariri, who threw Lebanon into political crisis by reading out his resignation on November 4 from Riyadh, said on Sunday he planned to return within days.
UN Secretary-General Antonio Guterres warned Friday that a new conflict in Lebanon would have "devastating consequences" and said he was engaged in intense contacts with all players to urge de-escalation.
The head of Lebanon's powerful Hezbollah movement on Friday said Saad Hariri, who resigned as Lebanese prime minister from Riyadh last week, was "detained" by Saudi Arabia.