But opposition parties in Algeria said it would not guarantee free elections.
Algerian police fired tear gas at crowds as they attempted to reach the presidency.
The renewed calls for regime change come just days after Lt Gen Gaed Salah demanded that Mr Bouteflika be declared unfit to rule.
What do the protesters want?
Demonstrations against Mr Bouteflika began last month after the president, who has seldom been seen in public since suffering a stroke in 2013, announced that he would stand for another term.
In response, the president agreed to not stand for a fifth term in upcoming elections, which have been delayed.
However the move did not go down well with protesters, who said his decision not to run was a cynical move to prolong his 20-year rule.
They are now calling for the departure of the president and also an entire generation of Algerian political leaders, including those who would be in line to succeed him.
At the protest in Algiers, one member of the crowd, named as Ali, told Reuters news agency: “We only have one word to say today, all the gang must go immediately, game over.”
What happens now?
Lt Gen Gaed Salah – who is also deputy defence minister and seen as loyal to Mr Bouteflika – this week called for the use of Article 102, which allows the Constitutional Council to declare the position of president vacant if the leader is unfit to rule.
The ruling party, the National Liberation Front (FLN), backed the general’s call.
Under the constitution, the head of the Senate, Abdelkhader Bansallah, would become the acting head of state until an election could be held.
Despite the significant intervention, the call from the army chief of staff does not appear to be enough for protesters and opposition parties, who have continued to protest on the streets.