In at least one location, police opened fire with tear gas and rubber bullets, chasing and beating demonstrators, after youths hurled stones at them, a journalist said.
The huge turnout came days after the military called for the long-serving leader’s removal to end a growing political crisis. State TV showed protests in several other cities as well.
The protests have been largely peaceful but have put pressure on the army to stabilise the country.
While many people are against Bouteflika and his shrinking inner circle, they also reject the army’s intervention in civilian political life.
“Street pressure will continue until the system goes,” said student Mohamed Djemai, 25, as hundreds of riot police kept an eye on the protests and helicopters flew overhead.
“We have only one word to say today, all the gang must go immediately, game over,” said Ali, a merchant, as other protesters shouted “the people want the fall of the regime”.
Families stood on balconies above the streets cheering the marchers — Algerians of all social classes, including journalists, doctors, teachers and homeless people.
The crowds shared out dates and water and bought ice cream from street vendors.
The army chief of staff, Lieutenant General Ahmed Gaed Salah, on Tuesday asked the constitutional council to rule whether the ailing 82-year-old president is fit for office.
The move further isolated Bouteflika, who has failed to placate Algerians by reversing a decision to seek a fifth term.
Key allies have deserted the head of state, who has rarely been seen in public since suffering a stroke in 2013 and now faces the biggest crisis of his 20-year-old rule.
Protesters have ambitious demands in a country long- dominated by veterans of the 1954-1962 independence war against France, now seen by many Algerians as too old and out of touch.
They want to replace the establishment with a new generation of leaders capable of modernising the oil-dependent state and giving hope to a population impatient for a better life. “You are Titanic. You will sink,” protesters shouted.
The powerful military has stayed in the barracks throughout the unrest.
“There is a risk in involving soldiers in the protests because the soldiers are young. They could end up not listening to orders to confront protesters,” said a former military intelligence officer.
But Salah’s call for Bouteflika to go was a clear reminder to Algerians that the army intends to retain its vast influence in national affairs.
Saadia Belaid, a woman crying as she wore the flag of Algeria, said: “I cry because they kidnapped Algeria and the army’s proposal is a real travesty.” “We want the departure of Salah,” read a banner.
Salah’s call, however, received backing from the ruling FLN party and the main trade union, signalling that Bouteflika’s time was all but up.
In the latest blow to Bouteflika, one of his few remaining influential supporters, leading businessman Ali Haddad, resigned as head of the influential FCE business forum.
Haddad, who was awarded large public works projects by the government and has investments in the media, has helped to fund Bouteflikas election campaigns over the years.
“Corrupt people must go. We are determined to clean the country,” said post office employee Noueddine Menar, 33.
Under the constitution, the chairman of parliament’s upper house, Abdelkader Bensalah, would serve as caretaker president for at least 45 days after Bouteflika’s departure. But even if Bouteflika quits, there is no clear long-term successor.