"The President of the Church of the Protestants, in particular the young people," said the president in a statement on national television on Sunday evening.
"I pledge not to be a candidate in that election which will ensure I am succeeded in undeniable conditions of serenity, freedom and transparency," the letter read.
Bouteflika, who is celebrating his 82nd birthday on Saturday remains in Geneva for medical treatment.
The veteran leader uses a wheelchair and has rarely been seen in public since 2013.
Bouteflika's decision to run for a term of office Abdelghani Zaalene.
Enduring support vs rising anger
Zaalene pointed out that the president is still very popular and has garnered more than 5 million sponsors.
Bouteflika 's bid to placate demonstrators came after the largest number of Algerians.
In his statement, Bouteflika vowed that if he won a fifth term, he would organize an inclusive, independent national conference, which would select a date for the early presidential election.
He also promised to make a referendum to modify the constitution.
Moreover, he said he would oversee a redistribution of national wealth.
The announcements failed to appease protesters, who held rallies that lasted late in the night against Oran, Tiaret and Constantine.
"It's exactly what happened in 2011-2012 after the so-called Arab Spring," Algerian sociologist Nasser Djabi told RFI. "But the people saw it just because it did not really change.
"The political system in Algeria is blocked." So people will be constantly asked, "Is this the same thing? Will the same scenario repeat itself?"
Doubt over Bouteflika's candidacy
Bouteflika's candidacy will be accepted, after Abdelwahab Derbal, president of the Independent Election Monitoring Committee (HIISE), declared that all candidates "must file their applications in person".
The Algerian press agency, APS, reported that Bouteflika 's campaign director had filed his candidacy for him on Sunday, a few hours before the deadline.
Naoufel Brahimi El Mili, a professor of politics at Sciences Po University in Paris, says Bouteflika's failure to present his candidacy in the past.
Speaking to RFI's partner station, FRANCE 24 , he dismissed the president's offer of snap elections to 'souk bargaining tactics' aimed at securing himself a smooth exit from power without losing face.