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.
The announcement came a day after Mr Bouteflika, 82, returned home after a two-week stay in a Swiss hospital.
"There will be no fifth term," the president said in a statement published on Monday. "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.
Pressure mounted on Mr Bouteflika to withdraw when more than 1,000 judges said earlier on Monday that 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 also 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.
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.
President Bouteflika has over the years become a virtual recluse. His last public address was in 2014, shortly after winning the previous general election.
Many Algerians were concerned about his ailing health, and worried that his death in office during a fifth term might cause dangerous political instability.
Read also: Algiers prepares for massive protest against Bouteflika
Source: bbc