Proposal calls for the new office to be headed by a prominent legal figure who would be subordinate to the attorney general.
Former Prime Minister Ehud Olmert among dozens being charged in most serious graft case in Israel's history.
Former Jerusalem Mayor Ehud Olmert, among those indicted, did not attend Monday's hearing, as he appeared at another hearing on corruption and fraud charges in the Jerusalem District Court.
16 former Jerusalem municipal officials and business people charged with taking bribes to advance the Holyland luxury construction project in the capital.
Official responsible for monitoring the state prosecutor's office will be a prominent legal figure appointed by the attorney general, serving as an outside consultant.
Ofir Kalfa sought to move to new neighborhood in Kibbutz Gevim with his family; The Kalfkas petitioned High Court against law allowing some communities to screen potential residents.
Grunis' path to the Presidency was fraught by political controversy, with opposition parties criticizing the so-called 'Grunis law' geared at ensuring the veteran's judge selection to the lofty post.
The fire claimed lives of 44 people in all, including prison service cadets, prison guards, police commanders, one adult civilian and one teenaged volunteer.
Sources say Joseph Shapira currently enjoys the broadest support within the legislature, which is the body that chooses the state comptroller.
Overturns lower court ruling in case of officer who killed Palestinian girl.