Archbishop Aristarchus of Constantine, general secretary of the Patriarchate, said he would support all efforts for justice, according to the official Wafa news agency.
Both the government and the Palestinian parties accused Tel Aviv of the new crime that took place on May 11th.
The Palestinian Authority announced an investigation into the case and invited international human rights organizations to participate to that end, but categorically refused a joint investigation with Israel.
His death unleashed a wave of international condemnation of Israel, including from its allies.
In fact, more than 120 artists, including Susan Sarandon, Mark Ruffalo and Roger Waters, have called for sanctions against Israel over the murder.
We are deeply troubled by the crime, said a letter also signed by American musician Tom Morello and Spanish film directors Pedro Almodóvar and British filmmaker Ken Loach.
The letter is also signed by Mike Leigh, Tilda Swinton, Asif Kapadia, Miriam Margolyes, Carol Morley, Boots Riley, Jim Jarmusch, Steve Coogan, Naomi Klein, Hany Abu Assad and Peter Gabriel, among others.
Last week, the Israeli newspaper Haaretz revealed that the army had refused to open a criminal investigation into the circumstances of the death.
According to the newspaper, Yifat Tomer Yerushalmi, general defender of the corpse, decided to shelve the matter, arguing that after questioning the soldiers, there was no suspicion of a crime.
Although Israeli Prime Minister Naftali Bennett initially blamed Palestinian militants for his death, other cabinet officials, including Defense Secretary Benny Gantz, later admitted they did not know who shot him.