Peaceful nationwide protests against Bouteflika have taken place since february 22, but the biggest demonstration to date took place Friday when hundreds of thousands of people flooded the streets of Algiers to call for change.
The president is expected to name prominent worldwide peacemaker Lakhdar Brahimi to head a new "national conference" aimed at setting an election date and drafting a new constitution.
The veteran leader, who uses a wheelchair and has rarely appeared in public since suffering a stroke in 2013, said he was responding to "a pressing demand that you have been numerous in making to me". Nevertheless, he had meant to stand again for the presidency, triggering demonstrations that were reminiscent of the Arab Spring eight years ago.
"I particularly understand the message given by youth, in terms of anxiety and ambition for their own future and that of the country", Bouteflika said in a message published by the Algeria Press Service.
Moreover, the longtime leader promised his fellow citizens a "new republic" that would be built by new generations of Algerians. The conference, due to finish its work by the end of 2019, will submit a new constitution to voters in a referendum.
A wily political survivor, Bouteflika fought in Algeria's independence war from France and is still appreciated for reconciling his deeply damaged nation after the bloodshed of the 1990s during a decade-long Islamic insurgency.
"For these reasons, we chose to continue our protest until the departure of this regime and all that symbolizes it".
Paul Manafort sentenced to additional 3 1/2 years in prison
The jury was unable to reach a verdict on 10 counts, including conspiracy to commit bank fraud and bank fraud. He said he was "ashamed and embarrassed" for the impact that the case has had on his family and friends.
National television broadcast footage on Monday night of Bouteflika in his trademark three-piece suit receiving several senior officials.
Demonstrators said Bouteflika does not intend to leave office immediately and is "illegally" prolonging his fourth term.
The United States said it backed the talks going on in Algeria and that it was "closely monitoring" reports elections had been postponed. In the meantime, Algeria will be governed by an interim government to oversee the country's day-to-day institutional function.
Cars honked horns and families poured out into the streets.
"We announce our intention to abstain from. supervising the election process against the will of the people, which is the only source of power".
Concerns over Bouteflika's health began during his second term in 2005, when he secretly entered the Val de Grace military hospital in Paris for a bleeding ulcer.
The delay could help to ensure a peaceful transition of power - allowing all candidates to campaign properly while addressing the public's core demand of removing Mr Bouteflika from office.