The original bill proposal was that the power to elect the watchdog would shift from the judicial selection committee to the Knesset.
Since May 2024, the position of Ombudsman of the Judiciary has remained vacant.
The new proposal also includes a mechanism to prevent a stalemate in high court appointments.
"This is a sad day for democracy and a sad day for our judicial system," the justice minister said in a statement.
The Judicial Selection Committee convenes to appoint Israel's new chief justice.
The bill proposal, by Likud MK Osher Shkalim, is one of a number of proposals targeting Kan, which are being promoted by Communications Minister Shlomo Karhi.
Earlier on Friday, Attorney-General Gali Baharav-Miara penned a letter to Levin, calling on him to convene the committee.
The ultra-Orthodox IDF draft has come to a head as the Israel-Hamas war has seen reservists completing hundreds of days of duty. IDF says it needs more manpower to deal with the new security reality.
The final tally was 53-45 against the proposal. However, the coalition has attempted to come up with an alternative committee.