Key parties have jostled over ministries since a legislative vote in May, as officials and foreign donors warned that a delay would aggravate the country's economic troubles.
Saad al-Hariri was speaking after meetings with lawmakers over the make-up of the new coalition to be formed after a May 6 parliamentary election.
In a post-election speech last week Hariri said the party had been expecting a better result and there had been "gaps" in how it conducted its campaign, for which people would be held responsible.
Lebanese began voting on Sunday in their first general election for nine years, one that is seen as unlikely to upend the country's basic contours of power but is important for economic stability.
Lebanon's Prime Minister Saad al-Hariri has been invited to Saudi Arabia, his office said on Monday, setting the stage for his first visit since he abruptly resigned there in November.
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.
Saad al-Hariri attended independence day celebrations in Beirut on Wednesday after returning to Lebanon for the first time since resigning as prime minister in a broadcast from Saudi Arabia.
Regional tensions have risen in recent weeks between Saudi Arabia and Iran over Lebanese Prime Minister Saad al-Hariri's surprise resignation and after an escalation in Yemen's conflict.
Lebanon's Foreign Minister Gebran Bassil said on Friday a crisis triggered by the resignation of its prime minister was part of an "attempt to create chaos in the region", local television stations reported.
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.
President Emmanuel Macron has invited Lebanon's Saad al-Hariri and his family to France, the French presidency said in a statement.