Thousands of Algerians are gathering for the sixth successive Friday of mass anti-government protests.
Earlier this week, Lt Gen Ahmed Gaed Salah called for the position of president to made vacant.
But opposition parties in Algeria said it would not guarantee free elections.
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 to the demonstrations, the president later agreed not to stand for a fifth term in upcoming elections, which have been delayed.
Protesters called this a cynical move to prolong his two-decade rule and are now calling for the departure of not just the president, but also an entire generation of Algerian political leaders, including those who would be in line to succeed him.
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 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.
By Adekunle Best, BBC Newslight Africa
Opposition parties and protesters in Algeria were not impressed by the suggestion of Lt Gen Gaid Salah to trigger Article 102 of the constitution.
The majority of protesters are youth who are not involved in party politics and who say they are not interested in the departure of Mr Bouteflika only to see the power transferred to his former allies – bringing to power different faces of the same regime.
It is difficult to predict what is going to happen because there is no indication that opposition parties hold any influence over the protesters, who do not have any leader or spokesperson who could hold talks with the authorities.
The army clearly wanted to see an end to the crisis when they abandoned Mr Bouteflika in an unexpected move. But they need to find an influential party to discuss the procedure with.
For the moment, the protesters’ expectations are very high as they demand the departure of “everybody who has been associated with the regime”, but they do not offer an alternative.
Lt Gen Gaid Salah had already dismissed the idea of “removing everybody” as expressed in the protests and on social media.