0623 GMT January 26, 2020
Bouteflika, who returned to Algeria on Sunday after medical treatment in Switzerland, has watched one long-time ally after another join mass demonstrations calling on him to step down, Reuters reported.
Now in their third week, the protests have seen Algerians desperate for jobs and angry about unemployment and corruption demonstrate in towns across around the vast North African country against Bouteflika's bid for a fifth term in office.
The marches have shattered years of political inertia and unsettled Algeria's opaque but powerful security establishment.
In a statement, the judges added their voice to the protests by announcing the formation of a new association "to restore the gift of justice".
"We announce our intention to abstain from ... supervising the election process against the will of the people, which is the only source of power," the judges said in a statement.
The statement drew a sharp retort from Algerian Justice Minister Tayeb Louh, a member of Bouteflika's inner circle, who said judges should remain neutral.
In another setback for the president, who plans to stand in elections in April, clerics told the minister of religious affairs to stop pressuring them to issue pro-government sermons.
"Leave us to do our job, do not interfere," cleric Imam Djamel Ghoul, the leader of an independent group of clerics, said in remarks to reporters.
The 82-year-old Bouteflika faces the toughest fight of his 20-year-old rule, following a tenure in which he became the north African country's most powerful president in 30 years.
In Algiers, tens of unionists staged a protest rally outside the headquarters of the main union, UGTA, calling on its leader Abdelmadjid Sidi Said, a Bouteflika ally, to resign.
The veteran head of state has rarely been seen in public since a stroke in 2013. Last April, he appeared in Algiers in a wheelchair.
In the clearest indication yet that the army is seeking to put some distance between itself and Bouteflika, the chief of staff said the military and the people had a united vision of the future, state TV reported. Lieutenant General Gaed Salah did not mention the unrest.