Current Interior Minister Nouredine Bedoui will replace Ahmed Ouyahia, who resigned as prime minister on Monday after the president's decision of not standing for election, the state news agency APS reported. "We defeated the supporters of the fifth term!" said taxi-driver Mohamed Kaci, 50. The decision to run for a new term in the April 18 election angered large swathes of Algerian society.
Bouteflika postponed the April presidential election Monday and withdrew his candidacy.
The president returned Sunday from two weeks in a Geneva hospital, but his health problems and overall condition remain unclear.
While Bouteflika and the country's armed forces neutralized Algeria's Islamic insurgency, they then watched it metastasize into a Sahara-wide extremist movement linked to smuggling and kidnapping - and to al-Qaida.
Algerian President Abdelaziz Bouteflika seen voting at a polling station in the capital Algiers during polls for local elections in 2017.
"France expresses its hope that a new dynamic that can answer the deep aspirations of the Algerian people will rapidly take hold", Foreign Minister Jean-Yves Le Drian said in a statement.
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However, in his letter, the President announced that a "national conference" would be tasked with planning the vote and would be drafting a new constitution for the country.
President Bouteflika rarely appears in public and has not given a public address since having a stroke in 2013.
The protests are not expected to abate anytime soon, with another demonstration scheduled for Friday.
Last month, Algeria's ruling National Liberation Front nominated Bouteflika - who has ruled Algeria since 1999 - to run for office. 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.
Emmanuel Macron, president of Algeria's former colonial ruler France, said Bouteflika's decision opened a new chapter and called for a "reasonable duration" to the transition period.
"On paper, two ways are possible", a source close to Bouteflika's campaign team told Middle East Eye.
"We have taken to the streets today to protest a fifth presidential term".
Algerians took to the streets of Algeria, chanting "this is a republic, not a kingdom" and "20 years is more than enough". In the meantime, Algeria will be governed by an interim government to oversee the country's day-to-day institutional function.