Bouteflika, 82, abandoned his bid for a fifth term in power on Monday, bowing to weeks of rallies against his 20-year rule by people demanding a new era of politics in a country dominated by an old guard.
Crowds celebrated late into Monday night and were back on the streets of central Algeria on Tuesday chanting: "We want this system to go".
"The whole system must disappear immediately. Our battle will continue," said Noureddine Habi, 25.
After meeting the president on Monday, Brahimi praised protesters for acting responsibly, saying on state television that it was necessary to "turn this crisis into a constructive process".
Algerians have grown tired of the ailing leader and other veterans of the 1954-1962 war of independence against France who have dominated a country with high unemployment, poor services and rampant corruption.
French President Emmanuel Macron said Bouteflika's decision opened a new chapter and called for a "reasonable duration" to the transition period.
Algeria's powerful military is expected to play a behind-the-scenes role during the transition and is currently considering several civilians as candidates for the presidency and other top positions, political sources said.
One of them includes a prominent lawyer and activist Mustafa Bouchachi, who has gained a wide following on Facebook during the protests.
LEAVE A COMMENT Your email address will not be published. Required fields are marked*
Togo President Gnassingbe wins re-election in landslide: preliminary results
Lesotho PM in court to be charged with murder of ex-wife
Togo counts votes as challenger claims ‘fraud’
Troops at home of Togo opposition candidate as presidential polls close
Togo votes as president seeks likely fourth term
Ethiopia plans to release interim jet crash report as probe continues
South Sudan's former rebel leader sworn in as first vice president
Togo votes as Gnassingbe seeks to extend dynasty's half-century rule
Lesotho PM a no-show for murder charge