After initial celebratory rallies, thousands of students held a fresh protest in the capital Tuesday, accusing Bouteflika of "tricks".
President Bouteflika rarely appears in public and has not given a public address since having a stroke in 2013. Bouteflika's critics question whether it is legal to unilaterally declare the postponement of national elections would be postponed - and they're now left to wonder what will happen when the president's current term expires on April 28.
In a letter addressed to Algerian citizens on Monday, Bouteflika announced the holding of the presidential election as an extension of the "inclusive and independent" national conference and the "formation of a government of national competences".
After years in office, Bouteflika's powerful political machine had the constitution changed to cancel the presidency's two-term limit.
Algeria's president says he is creating a new government and a special body to draft a new constitution to respond to mass protests.
Bouteflika has named interior minister Noureddine Bedoui as the new prime minister to replace the unpopular Ahmed Ouyahia. "There have also been demonstrations against Bouteflika in cities across France, home to the world's largest Algerian diaspora".
Veteran diplomat Lakhdar Brahimi and protest groups are expected to join a conference planning Algeria's future that Bouteflika said should try to finish its work by the end of 2019, government and political sources told Reuters.
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Several FLN parliamentarians resigned on Friday to join the protest movement. But critics on Algerian social media Tuesday dismissed him as a symbol of a has-been generation and member of the global elite who has spent too much time overseas to understand Algeria's current reality. Should the election process descend further into chaos, it is possible that the military will step in, akin to the Egyptian military's action during the country's 2011 protests.
On Sunday, thousands took to the streets of the capital carrying the Algerian flag and chanting: "Bouteflika, there will be no fifth term".
French President Emmanuel Macron said Bouteflika's decision opened a new chapter and called for a "reasonable duration" to the transition period.
"In the place of a fifth term, he is extending his fourth term".
In 20 years as president, however, age and illness took its toll on the once-charismatic figure.
"Second: There will be no presidential elections on the coming 18th of the coming April".
Said Bouteflika, 61, a brother of the president and top aide, is said to hold enormous influence in the presidential apparatus.