The Algerian president, Abdelaziz Bouteflika, has withdrawn his bid for a fifth term in office after mass protests against his rule and postponed elections scheduled for April to allow for consultation on reforms “for a new generation”.

Bouteflika made the surprise announcement on Monday in a letter to the Algerian people released by his office. The 82-year-old leader, who has been in power for two decades, acknowledged three consecutive weeks of demonstrations against his rule in which hundreds of thousands of people from across Algerian society took to the streets.

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“I understand the motivations of the many people who chose this method of expression,” Bouteflika said in the letter, praising the peaceful nature of the protests before promising sweeping constitutional and political changes.

“This new system and new republic will be in the hands of a new generation of Algerians,” he said, promising a national conference lasting until the end of this year to find his successor.

Video posted online showed stunned citizens in Algiers’ central Audin Square waving their arms with joy to a chorus of celebratory car horns.

“It is great news! I’m both happy and confused because there’s still so much more that needs to happen,” said Nourhane Atmani, a student who took part in the protests. “Refusing Bouteflika’s fifth bid was just a step. The people need to unite to choose what’s next.”

As Bouteflika made his announcement, the prime minister, Ahmed Ouyahia, resigned and was replaced by Noureddine Bedoui, previously the interior minister, Ennahar TV reported on Monday. Ramtane Lamamra, who was Bouteflika’s diplomatic adviser, was appointed deputy prime minister, it said.

Bouteflika arrived back in Algeria late on Sunday night after two weeks of medical treatment in Geneva, returning to a country beset by protests and a general strike. Last Friday hundreds of thousands of people took to the streets, marking the third week of demonstrations against his rule.

What began as protests against his bid for a fifth term as president quickly expanded into opposition to the entire regime around the infirm leader, and some young demonstrators said on Monday they were not entirely satisfied with Bouteflika’s proposal.

“It’s one small battle won,” said Yasmine Bouchene, of the collective Les Jeunes Engagés (Activist Youth). “Bouteflika asked for another year and he got his way. But we are willing to keep on fighting,” she said.

There is widespread resentment at the perceived incompetence and corruption of the Front de Libération Nationale (FLN), the party that has been in power for more than 50 years. Several FLN parliamentarians resigned on Friday to join the protest movement.

Bouteflika had previously warned protesters of the risk of infiltration by “misleading parties” leading to chaos not seen since the civil war. He had offered to hold another election to choose his successor if re-elected in April.

But in the letter on Monday night, Bouteflika cancelled the 18 April vote. 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”.

Bouteflika said the government would organise a national conference under the direction of an independent presidential commission. “This will independently decide the date of the presidential election, in which I will not be a candidate in any instance,” he said.

The conference will be accompanied by a national referendum to rewrite the constitution. In the meantime, Algeria will be governed by an interim government to oversee the country’s day-to-day institutional function.

Raouf Farrah, of Les Jeunes Engagés and Ibtykar, an organisation to promote civil engagement, said: “For me, this is not a victory. Delaying the elections doesn’t mean they’re cancelled; it’s a tactic to maintain the status quo, at least temporarily.”

Farrah did not trust the outgoing president’s promises. “Bouteflika can still remain in power until the end of the so-called national conference, with no guarantees or a timetable. He wants to steal victory from the people by claiming to be the saviour of Algeria,” he said.

Mustapha Bouchachi, a human rights lawyer, described the announcement as a “half victory.”

France’s foreign minister, Jean-Yves Le Drian, praised Bouteflika’s declaration and said France was “hopeful that a new momentum to reward the highest aspirations of the Algerian people will quickly emerge”.

A five-day general strike began on Sunday as shops across the country were closed and groups of workers gathered in the streets brandishing flags and signs objecting to Bouteflika’s attempt to serve a fifth term in office.

Despite the government’s efforts to contain the protests, some workers in the energy sector, which accounts for an estimated 30% of the country’s GDP, joined the strike on Sunday, the first day of the working week in Algeria.

Social media posts implored citizens to enact civil disobedience and refuse to attend their jobs for the rest of the working week.

It was unclear on Monday evening whether the strike would continue, but some protesters pledged to maintain pressure on the government by demonstrating again on Friday this week.

“The people have been asking to bring down the whole system – this is a small victory compared to what people are asking for,” said Tin Hinane el-Kadi, a member of the protest movement Mouwatana.

“When you think about it, what Bouteflika wrote is basically something we rejected before,” she said. “He’s illegally extending a fourth term and staying until the end of the year, and we don’t want that. We’re asking for democracy, a state of law and a change of regime – we want the current to go, so this is clearly not enough. People will still be protesting on Friday,” she said.