0522 GMT May 22, 2019
In a surprise announcement Monday, the 82-year-old leader said he would not stand for a fifth term and cancelled next month's presidential election, AFP reported.
After initial celebratory rallies, thousands of students held a fresh protest in the capital Tuesday, accusing Bouteflika of "tricks".
"The students are resisting the extension of the fourth mandate," they chanted at the rally in a square outside Algiers' main post office which some teachers also joined.
Half a dozen police vans were parked around the Place de la Grande Poste, which has been the epicenter of protests demanding Bouteflika resign.
"Bouteflika has no right to prolong his mandate without the people's approval," said 22-year-old geology student Riad Labed.
"It's a ploy to win time... in order to put in place another puppet like the (current) president," said Amel, another student who only gave her first name.
Protesters held up signs saying: "No extra time. This is not a football match."
Students also took to the streets of second city Oran, local journalists said, while in the northeastern city of Annaba they were preparing for their next move.
The president announced on Monday that a "national conference" would set a new date for polls that he would not contest.
"There will not be a fifth term" and "there will be no presidential election on April 18", he said in a message.
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".
National television broadcast footage on Monday night of Bouteflika in his trademark three-piece suit receiving several senior officials.
Students have been at the forefront of weeks of massive demonstrations demanding Bouteflika step down, in a country where half the population is under the age of 30.
Messages posted overnight on social media urged students across the country to "end this system, end this mafia" with more protests planned on Friday.
"No to manipulation, let's be vigilant. The battle is not won. Those in power want to stay and proof of this is that the interior minister has become the prime minister," one message said.
Bouteflika has named Interior Minister Noureddine Bedoui as the new prime minister to replace the unpopular Ahmed Ouyahia.
Several newspapers have also accused Bouteflika of deceiving the people.
"He scraps the presidential election but stays in power: the latest ploy by Bouteflika," the influential El Watan newspaper said on its front page.
The Liberte daily denounced a "sham" while El Khabar newspaper said Bouteflika wanted "to remain president without elections".
Former colonial power France cautiously "welcomed" Bouteflika's announcement but President Emmanuel Macron called for "a transition in a reasonable timeframe".
Bouteflika's mandate officially ends on April 29.
But his promise on Monday of a "national conference" to carry out reform and set a date for new elections "before the end of 2019" suggested he may stay in office for another year.