Thirteen independent Algerian unions have refused to back the newly-appointed prime minister's efforts to form government.
Prime Minister Noureddine Bedoui hopes his new government will placate protesters who are pressuring President Abdelaziz Bouteflika to step down.
"We will not hold discussions with this system, we belong to the people and the people said 'No' to the system," Boualem Amora, one of the leaders of the education sector unions, told reporters.
Bedoui has promised to create an inclusive government of technocrats, taking in the military and business representatives, in a country dominated by veterans of the 1954-1962 war of independence against France.
But union leaders said they refused to enter a dialogue when he reached out to them.
Many Algerians, who have been demonstrating for more than three weeks, have rejected overtures by Bouteflika, 82, who has reversed a decision to stand for another term after 20 years in power.
Since returning from medical treatment in Switzerland the president has in recent days been losing allies, including senior members of the ruling National Liberation Front party, known by its French acronym FLN.
Australian Associated Press