The conference will supposedly draft a new constitution and reschedule the election.
"No to manipulation, let's be vigilant. I'm both happy and confused because there's still so much more that needs to happen", said Nourhane Atmani, a student who took part in the protests.
"I believe it profoundly", replied Algeria's newly named vice prime minister, Ramtane Lamamra, who some speculate might succeed Bouteflika as president, when asked whether his country was marking a turning point.
He stopped short of stepping down immediately - and crowds who took to the streets of Algiers again on Tuesday said they wanted a quick transition. "The battle is not won".
Following the announcement, the president said the election - which had been set for April - would be postponed, but did not set a new date.
The unprecedented citizens' revolt began last month and has drawn millions into the streets of cities across the country to say no to a fifth term for their 82-year-old president - and no to a system blamed for corruption and keeping Bouteflika in office despite his ailments.
Protesters claimed the move was proof that "those in power want to stay".
The global reaction was comparably upbeat, as French President Emmanuel Macron proclaimed the beginning of a new chapter in Algerian history, provided the transition period has a "reasonable duration".
Algerian president returns home after 'routine medical checks' in Geneva
Born in the border town of Oujda, Morocco, Bouteflika became one of his country's most enduring politicians.
The president announced on Monday that a "national conference" would set a new date for polls that he would not contest.
On Friday, Algerian businessman Rachid Nekkaz, who had unsuccessfully tried to stand as a candidate in the upcoming elections, was arrested after staging a protest with several dozen supporters outside HUG and then pushing inside to demand information about Bouteflika's condition. "Given that his very presence within the vote was unconstitutional", she said, "the vote itself could never really be legal".
Bouteflika also failed to create an economy that could offer enough jobs for Algeria's growing youth population despite the nation's vast oil and gas wealth.
"To tell the Algerians that he understood their message, it was necessary that heads fall", said a former executive of the FLN, the ruling party. In the meantime, Algeria will be governed by an interim government to oversee the country's day-to-day institutional function.
Former culture minister Abdelaziz Rahabi tweeted that Bouteflika was "ridiculing the people". "His unhealthy obsession with power is a threat to the stability of the state and the unity of the nation".
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