Algerian state news agency APS says President Abdelaziz Bouteflika has named the interior minister in his government as the new prime minister.
Interior Minister Noureddine Bedoui is close to the president's brother. Bouteflika charged Bedoui with forming a new government on Monday.
Bedoui is replacing Ahmed Ouyahia as prime minister.
Earlier Monday, Bouteflika said he was withdrawing as a candidate in the presidential election set for April. He was seeking a fifth term after 20 years in power.
The longtime leader also postponed the election and said he planned to put interim leaders in place to plan and reschedule the vote.
Bouteflika did not give a possible date or timeline for the election.