Algeria’s ailing president has promised to step down after the next election and enact reforms, as the nation’s elite moved to consolidate its power in the face of historic mass protests.

“I’ve heard the heartfelt cry of the protesters,” said Abdelaziz Bouteflika in a letter read out on national television on Sunday night. Addressing the uprising against his rule for the first time, he promised that, if re-elected in April, he would hold a national conference to implement political reforms and set a date for a second election where he would not be a candidate.

“[This] will find my successor in a manner incontrovertibly peaceful, free and transparent,” he said, adding that he would hold a national referendum to adopt “a new constitution which will mark the birth of a new republic and a new Algerian political system”.

An estimated 6,000 Algerians protested in Paris on Sunday, while thousands of students took to the streets in Algiers. Observers waited to see if Bouteflika would return from medical treatment in Geneva to submit his candidacy before Sunday’s midnight deadline.

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Tens of thousands of Algerians protested across the country on Friday to demand that the 82-year-old leader renounce his bid for a fifth term. Bouteflika has made few public appearances or speeches since suffering a stroke in 2013, fuelling speculation that the country is effectively run by his brother and adviser, Saïd Bouteflika, along with the head of the military, Ahmed Gaïd Salah, and a cabal of opaque political and military officials known as le pouvoir or “the power”.

In a sign of tensions at the top and the regime’s determination to maintain power, Bouteflika suddenly sacked his campaign manager, Abdelmalek Sellal, on Saturday. He was replaced by Abdelghani Zalène, a former transport minister, who did not respond to a request for comment when contacted by the Guardian.

Rumours have been rife that the Algerian elite would seek to replace Bouteflika with another candidate to ensure the long-term survival of the regime he has headed since 1999, but there was little to suggest on the day of the deadline that the president and his entourage would cede to the demands of the protesters.

Stephen McInerney, of the Washington-based thinkthank Project on Middle East Democracy, said: “For months, there’s been speculation that the elites would make some kind of effort to find a successor to Bouteflika, but the announcement that he would run again was widely interpreted as a sign of a failure to do so. It seems there was only consensus around keeping Bouteflika and fears that moving on would disrupt the status quo that le pouvoir is happy with.”

Others submitted their candidacy on Sunday, including the former general Ali Ghediri and Rachid Nekkaz, a pro-business candidate. He had previously claimed that he had been held under de facto house arrest to prevent him from campaigning, but he travelled to Algiers to present the required number of signatures. He later told the Guardian he was forcibly returned to his village after leaving the constitutional court, but did not say whether he had submitted his candidacy.

According to Swiss news reports, Bouteflika was remaining in Geneva for medical treatment. Dictator Alert, a bot that tracks air traffic at Geneva airport, said on Twitter that an Algerian government plane had landed on 24 February, departed less than an hour later and “hasn’t been seen since”.

Algerian law requires candidates to submit 60,000 signatures in person, leaving many to wonder whether Bouteflika was well enough to return and submit his candidacy in Algiers. “The candidate must present the signatures themselves,” said Abdelwahab Derbal, head of the country’s electoral monitoring body, in response to reports that Bouteflika’s new campaign manager would present his candidacy in his place and read a letter from the president.

Late on Sunday afternoon, eight vans carrying the required signatures arrived at the constitutional court in Algiers to confirm Bouteflika’s candidacy but without any official present, an act likely to further provoke the ire of demonstrators who view him as unfit to rule.

“If Bouteflika continues to run, Algeria risks sliding into chaos,” Omar Belhouchet, the founding editor of the Algerian newspaper El Watan, told France 24. He said Bouteflika’s attempt to hold on to power was “totally unrealistic”.

McInerney said: “Every step the regime takes is increasing the anger and frustration of people on the streets. This is potentially a dangerous scenario. Right now, the streets want anyone else other than Bouteflika as president. Each day that passes, they want even more,” he said.