Fractious political leaders, in power for decades, have traded blamed for hindering progress as Lebanon sinks into its worst crisis since its 1975-1990 civil war.
Under the French roadmap, the new government would take steps to tackle corruption and implement reforms needed to trigger billions of dollars of international aid.
Last week's clashes in Khaldeh between Sunni Muslims and Shia's, in which a 13-year-old boy was killed, had prompted a flurry of contacts among Lebanese politicians.
The Lebanese army and the security source said gunfire was exchanged.
Senior US official David Hale is expected in Beirut later on Thursday to stress the urgent need for financial and governance reforms, ending endemic corruption and bringing transparency.
Lebanon must be considered a failed state, going back to the 1989 Taif agreement to end the civil war.
"Today we follow the will of the people in their demand to hold accountable those responsible for the disaster that has been in hiding for seven years, and their desire for real change."