Coming more than two weeks after anti-Bouteflika protests broke out across the North African country, the judges said in a statement published on Sunday that they were forming 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 statement read.
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.
"The independence and integrity of the judge must be consistent whatever the reasons," Ennahar TV quoted him as saying.
Lawyers on Monday launched a 48-hour walkout to demand the Constitutional Council reject Bouteflika's re-election bid on the grounds of "incapacity" to carry out the role.
The 82-year-old Bouteflika, who returned to Algeria on Sunday after undergoing medical treatment in Switzerland, faces the toughest fight of his 20-year rule.
The ailing head of state has rarely been seen in public since a stroke in 2013.
Bouteflika has offered to limit his term after the election and has vowed to change the "system" that runs the country. The promises, however, have failed to quell public anger, galvanising discontent among different sectors, particularly students and other young people.
Algerians from all social classes have rejected his plan to secure a fifth term in next month's elections, a move protesters feel would perpetuate a stale political system dominated by veterans of an independence war against France that ended in 1962.
"Bouteflika is back, we delivered a message, we need a response, and we need a response now,” Mouloud Mohamed, a 29-year-old pharmacist, told Reuters news agency.
The secretive military-based establishment known to Algerians as "le pouvoir" [the powers-that-be] appears to have stood aside while the demonstrations have taken place.
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.
Young Algerians are desperate for jobs and angry about unemployment and corruption and complain that their leaders still dwell on the victory over France instead of improving living standards for the future.
"This time, it's quite different. What we see now is a momentum that is building up across Algeria," Al Jazeera's Hashem Ahelbarra, who has covered the region extensively, said of the ongoing demonstrations.
"Many people believe if this momentum continues for the next two weeks, it could be a game changer," Ahelbarra added.
Looking ahead, Ahelbarra said a key date for the country was going to be March 13, when Algeria's constitutional committee is set to determine the legitimacy of the presented candidacies for next month's elections.