Buji's announcement came after a May 21 accord between the country's political opponents that spared Lebanon from a potential civil war, al-Alam reported.
The accord gave the parliamentary majority 16 cabinet seats and the opposition 11 cabinet seats.
Parliamentary majority leader Saad Hariri said he asked Prime Minister Fouad Siniora to "accept the nomination" of former head of the Syrian Social Nationalist Party, Ali Kanso.
It is reported Siniora has said he is against Kanso taking part in the Cabinet.
Celebrity Families of 2014 [PHOTOS]