Algerian President Abdelaziz Bouteflika has postponed the 18 April presidential elections and said he will not seek a fifth term in office.
President Bouteflika's candidacy had provoked mass protests across Algeria over the past few weeks.
He has led Algeria for 20 years but has been rarely seen in public since he suffered a stroke in 2013.
No new date for the election was set. A cabinet reshuffle will happen soon, a statement in Mr Bouteflika's name said.
There was no suggestion in the announcement that the president intends to step down before a rescheduled election.
Meanwhile, Algeria's Prime Minister Ahmed Ouyahia announced his resignation and was replaced by Interior Minister Noureddine Bedoui, who has been tasked with forming a new government, the official APS news agency reported.
"There will be no fifth term," Mr Bouteflika was quoted as saying in a statement. "There was never any question of it for me. Given my state of health and age, my last duty towards the Algerian people was always contributing to the foundation of a new Republic."He had pledged last week that he would step down early if re-elected - but the guarantee failed to placate the thousands of demonstrators. Algeria had been hit by strikes by teachers and students, as well as shops closing and train services being suspended as thousands took to the streets.
Pressure mounted on Mr Bouteflika to withdraw when more than 1,000 judges said on Monday they would refuse to oversee the planned general election were he a candidate.
Then the military's chief of staff, Lt Gen Gaed Salah, said the military and the people had a united vision of the future - the strongest indication so far that the armed forces were sympathetic to the protests.
Top clerics had already criticised pressure on them to issue pro-government sermons. "Leave us to do our job, don't interfere," cleric Imam Djamel Ghoul, leader of an independent group of clerics, told journalists.