The development comes as Iraq's Shiite-led government is mired in a war against the Islamic State group, which has captured a third of both Iraq and neighboring Syria.
The Iraqi forces and their Sunni and Shiite allies have struggled to claw back territory from the Sunni militant group despite US-led coalition airstrikes targeting the extremists.
Abdul-Sattar Bayrkdar, the spokesman for the Supreme Judicial Council, said council members rejected calls for Judge Medhat Mahmoud "to retire." The council is Iraq's highest legal authority, composed of experts in civil law and Islamic law, or Sharia, and it appoints Supreme Court judges. "The public interest and justice at this stage require him to stay in his duties," Bayrkdar's statement said.
Calls to dissolve the parliament and stop judicial corruption were among the demands of tens of thousands of protesters who took to the streets on Friday.
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Some also chanted against Judge Mahmoud, claiming he was "illegitimate."
Grand Ayatollah Ali al-Sistani in his Friday sermon said that reforming the judicial system was the most important step toward true reform.
"There is no real reform process without it," al-Sistani said through spokesman Abdul-Mahdi al-Karbalaie. Meanwhile, Iraq's parliament on Monday approved a report implicating senior officials over the fall of Mosul, Iraq's second-largest city, which the Islamic State captured in June last year.