A group of Algerians celebrated the development at Maurice Audin Square in the capital city of Algiers.
Algerians told the Dzair News channel they wanted “full change” to the government rather than “superficial regulations” as announced Monday by President Abdelaziz Bouteflika.
“All of them need to change. We don’t want any of them; neither [Noureddine] Bedoui nor [Ramtane] Lamamra,” protesters told the channel.
Prime Minister Ahmed Ouyahia handed his resignation to Bouteflika, who later appointed Bedoui in his place.
Meanwhile, Lamamra was appointed deputy prime minister.
In cities such as Jijel and Constantine demonstrators showed their joy by taking to the streets.
Meanwhile, some activists called for a continuation of weeks-long demonstrations until all of their demands, including a complete change to the system, are met.
Bouteflika postponed the April presidential election Monday and withdrew his candidacy.
The announcement came amid mass protests against his nomination seeking a fifth term that was slated for April 18.
Last month, Algeria’s ruling National Liberation Front nominated Bouteflika -- who has ruled Algeria since 1999 -- to run for office.
Since then, for a third consecutive week, thousands of Algerians in different parts of the country took to the streets to protest Bouteflika’s bid.
Opposition figures have repeatedly urged the aging president, who in 2013 was treated for a blood clot in the brain, to refrain from contesting the election.