Ben-Gvir tried to remove the Tel Aviv Police District commander from his position hours after criticizing Tel Aviv police treatment of protestors.
MQG head Dr. Eliad Shraga said that they were disappointed with the response to the petition, which deviated from her previous strictness on the matter.
A key part of Israel's judicial reform would change the composition and function of the Judicial Selection Committee.
NGOs had argued that since the coalition had expressed the desire to split the role of the attorney-general as part of the reform, she must have a conflict of interest in the matter.
Readers of The Jerusalem Post have their say.
According to the attorney-general, on a number of occasions, the national security minister attempted to intervene in operational events on the ground.
A preliminary police probe had been opened over a $20,000 wedding gift by Australian billionaire James packer in 2016.
The escalation between the coalition and Attorney General Gali Baharav-Miara lies in the dispute over whether the office has too much power.
The Impairment Law amends a provision in the quasi-constitutional Basic Law: Government and will now proceed to an initial Knesset vote.
In response, the attorney-general said that it was not possible to examine his request for self-representation against all petitions filed against him or his office.