The law in question would grant the coalition control of the Judicial Selection Committee.
The movement further stated it had requested the court to sanction Levin until he abides by the ruling and asked that a discussion be conducted on the subject.
The Justice Minister must name Chief Justice candidates by the end of the day.
The bill proposed to change the process to elect an ombudsman for Israel's court system.
This follows the petition submitted by the Movement for Quality government, which claims that the Justice Minister refuses to convene the Judicial Selection Committee.
According to his agenda, the justice minister intended for the committee to discuss sub-committees within it and determine rules for the committee's procedure.
Without new judges being appointed, Israel was on track to be short more than 50 judges by the end of next month.
The High Court is missing two justices after former chief justice Esther Hayut and former Justice Anat Baron retired last month.
It was decided that the ceremony would be a muted affair, with no speakers from outside the judiciary - and not just Justice Minister Yariv Levin.
NATIONAL AFFAIRS: May the questions over Israeli democracy and social divisions stay in 5783.