Many ministers already wanted to resign according to ministerial and political sources.
The information and environment ministers quit on Sunday as well as several lawmakers, and the justice minister also exited his role on Monday.
Finance Minister Ghazi Wazni, a key negotiator with the International Monetary Fund in a rescue plan to help Lebanon escape a financial crisis, prepared his resignation letter and brought it with him to a cabinet meeting, a source close to him and local media said.
The cabinet has decided to refer the investigation of the blast to the judicial council, the topmost legal authority whose rulings cannot be appealed, a ministerial source and state news agency NNA said.
The council usually takes on the top security cases.