Prime minister-designate Mustapha Adib is under pressure to form a fresh cabinet as soon as possible, so it can launch reforms required to unlock billions of dollars in foreign aid.
Lebanon was mired in its worst economic crisis in decades and battling the novel coronavirus pandemic even before a monster explosion at the Beirut port last month.
Appearing stooped and frail during a televised speech, the country's president warned prospects were looking glum.
"With the entrenchment of positions, no solution seems imminent," the 85-year-old said, stumbling on several words in his speech.
Asked where the country was headed if no agreement was reached soon for a new line-up, Aoun replied: "To hell, of course".
Lebanon's Adib earlier on Monday urged the country's myriad of political parties to rally together to rescue the country.
"Any further delay will exacerbate and deepen the crisis," Adib said in a statement, after a French-imposed deadline to form the cabinet passed last week.
"The Lebanese people's woes... require the cooperation of all sides," he said.
Adib's efforts to form a government have been effectively blocked by the two main Shiite groups in Lebanon's usual power-sharing arrangement -- Amal and Hezbollah.
Observers have said their insistence to keep the finance ministry under their control is linked to recent US sanctions against a former minister from Amal, as well as Hezbollah-linked businesses.
The August 4 explosion of hundreds of tonnes of ammonium nitrate at the Beirut port killed more than 190 people, wounded thousands, and ravaged large parts of the capital, prompting the previous cabinet to step down.