Bouteflika - who has ruled Algeria for decades - has faced three weeks of mass protests against his planned fifth-term run. Should the election process descend further into chaos, it is possible that the military will step in, akin to the Egyptian military's action during the country's 2011 protests.
"Right from the start he wanted to extend his term", she said.
Demonstrators gathered for hours in central Algiers before dispersing late afternoon.
The veteran leader, who has been in power since 1999 but whose rare public appearances since a stroke in 2013 have been in a wheelchair, returned Sunday from hospital in Switzerland.
National television broadcast footage on Monday night of Bouteflika in his trademark three-piece suit receiving several senior officials.
"We will march more determined than ever to end this system, to end this mafia".
Louisa Dris-Ait Hamadouche, a professor of political science at Algiers University, told AFP that Bouteflika's announcement was not an admission of defeat. The decisions announced yesterday are a partial victory for the people's movement. At the time, he said that if he won, he would call for new elections within one year.
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Algerians are also letting out pent-up anger at corruption that has left the country's oil and gas riches in the hands of a few while millions of young people struggle to find jobs. "We are now dealing with a president so eager to cling on power that he will stay in office until a date nobody knows".
Algeria's powerful military is expected to play its traditional behind-the-scenes role during the transition and is now considering several civilians as candidates for the presidency and other top positions, political sources said. He said this would calm tensions, allow the country to move forward along a path of "serene, calm and public security", and let Algerian institutions "prepare as quickly as possible for the advent of a new era in Algeria".
An election due to take place on April 18 will be postponed, an interim government formed and a committee appointed to draft a new constitution.
Others were more cautious, as Bouteflika gave no date or timeline for the delayed election.
Algeria's deputy prime minister said Boutiflika's decision was the most important turning point in since independence from France in 1962, Annahar TV reported.
Former culture minister Abdelaziz Rahabi tweeted that Bouteflika was "ridiculing the people".
Bouteflika managed to remain in power as the Arab Spring uprising toppled autocrats in neighbouring countries in 2011 because Algeria had enough foreign reserves to boost state spending.