With police standing back without intervening, the crowd at Algiers' landmark Grand Poste square was growing, hours before the scheduled start of a demonstration calling on the 82-year-old to step down after two decades in power.
The rally is the first major test of whether Bouteflika has calmed anger on the streets with his surprise announcement on Monday that he would not seek a fifth term but was cancelling an April presidential poll.
"You pretend to understand us, we will pretend to listen to you," read a banner held aloft by the mostly young demonstrators.
Bouteflika had initially sparked joy among protesters when he said he would not stand again, but his move to cancel the vote prompted accusations of "tricks" and sparked a new round of demonstrations.
He has also named a new prime minister, replacing unpopular premier Ahmed Ouyahia with former interior minister Noureddine Bedoui, who on Thursday defended the postponement of the poll.
Bouteflika, who uses a wheelchair and has rarely appeared in public since suffering a stroke in 2013, has promised a "national conference" to carry out reforms.
The president said that new elections would be held "before the end of 2019", suggesting he may stay in office for another year.
Algeria has largely avoided the turmoil unleashed by the Arab Spring uprisings that brought down rulers in neighbouring Tunisia and Libya.
But discontent, particularly among the young, turned to anger after the veteran leader announced on February 10 that he would seek another term.
Demonstrations have brought tens of thousands onto the streets for each of the last three Fridays, with smaller rallies taking place on other days.
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.
Several demonstrators on Friday said they had travelled from the Kabylie area, 100 kilometres (60 miles) east of Algiers, and spent the previous night with friends in the capital to avoid roadblocks or bus stoppages.
As at previous rallies after the weekly prayers, Algeria's ubiquitous red-white-green flag fluttered from windows and balconies of buildings leading to the city centre.
'Thanks for keeping people mobilised'
Algeria's new prime minister on Thursday sought to calm tensions ahead of the new demonstrations that could prove decisive for the protest movement.
Bedoui warned at a news conference that the situation was "sensitive" in the North African country.
People "must show calm and act peacefully", he said, calling for "dialogue" to resolve the situation.
Incoming Deputy Prime Minister Ramtane Lamamra has said that Bouteflika's proposed national conference on political reforms should take place "as soon as possible".
"The absolute priority is to reunite the Algerians and allow them to go together towards a better future," he said. "It's not about staying in power for a few weeks or a few months more."
But El-Watan newspaper on Friday fired back with a "Get Out" message to the new leadership, charging Bedoui had "ducked the real questions" facing the country.
The assessment was also harsh on social media, with one commentator in a tweet sarcastically thanking Bedoui and Lamamra for their "efforts to keep Algerians mobilised" for Friday's protests.
"Yesterday was the news conference of your prime minister and deputy premier, today is the news conference of the people," another critic of the regime wrote on social media.