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Thirteen Algerian unions have refused to back newly-appointed Prime Minister Noureddine Bedoui's efforts to form a new government.

Algeria's 82-year-old President Abdelaziz Bouteflika announced last week he will not run for a fifth term in office after weeks of protests against his latest bid.

Bouteflika also said he was replacing unpopular premier Ahmed Ouyahia with former interior minister Bedoui, who has defended the postponement of the poll, seen by many as unconstitutional. 

"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.

Bouteflika, 82, initially sparked joy among protesters when he said he would not stand for a fifth term in next month's election, but his move to cancel the vote prompted accusations of "tricks" and sparked a new round of demonstrations.

A huge crowd of demonstrators marched through the Algerian capital for a fourth consecutive Friday to step up demands on President Abdelaziz Bouteflika to leave, rejecting his offer not to seek re-election.

The protest movement has been led by students, in a country where half the population is under the age of 30 and youth unemployment has spurred anger against a government seen as out of touch.