Algeria is facing renewed street demonstrations this week after its constitutional council met to confirm the resignation of the president, Abdelaziz Bouteflika, as protesters expressed concerns over the caretaker government, saying the entire ruling regime should be replaced.

The resignation of the 82-year-old Bouteflika came after weeks of peaceful, unprecedented mass protests against his plans to run for another term as president after two decades in power. But the infirm leader – who has rarely been seen in public since a 2013 stroke and appeared pale and weak handing over his resignation letter – had long been seen as absent while an authoritarian and sclerotic clan known as Le Pouvoir (“The Power”) continued to rule. With slogans such as “Get them all out”, protesters said they wanted root-and-branch change of the close-knit ruling class marked by cronyism and corruption.

Many remained concerned that Lt Gen Ahmed Gaïd Salah, the head of the country’s powerful army, could seek to profit from a political vacuum at the top. The influential military, which has long been the backbone of Algeria’s regime, sought to position itself as on the side of the people by bringing forward Bouteflika’s resignation. Meanwhile, there was little trust in Abdelkader Bensalah, an ageing Bouteflika ally, who, as head of the current upper house of parliament, was confirmed as interim leader on Wednesday for a maximum of 90 days until an election.

“People understand that Bouteflika’s departure is just a step, an important one. But this is the start, and there is more to come,” said Tin Hinane El Kadi of Les Jeunes Engagés (Activist Youth). “People are demanding the departure of the whole regime, and will continue to take to the streets to demand the departure of known personalities, including Abdelkader Bensalah and Gaïd Salah. This will continue until the regime steps down.”

El Kadi also voiced concerns about the role of the military in the transition. “It’s clearly a worry and I think the intention is there from the army – Salah has played a very ambitious role and overstepped his duties. People don’t want to see history repeat itself,” she said.

Memories of a military coup in 1988 and decade-long civil war have stiffened the protesters’ resolve against any attempt at military rule. Despite Salah siding with the protests and encouraging Bouteflika to step down ahead of schedule, demonstrators remained determined to avoid an outcome similar to Egypt, where the president, Abdel Fatah al-Sisi, swept to power in a military coup after a popular uprising.

“The army is playing a dodgy game,” said El Kadi. “Gaïd Salah is saying he’s a friend of the people and the one who helped them win the fight. He’s positioning himself as an opponent, but anyone who knows Algerian politics knows he was Bouteflika’s best friend until a month ago.”

El Kadi feared that allowing the government to organise the upcoming election means it will be neither free nor fair.

International partners are watching closely to see how any transition would take place in the oil-and-gas-rich country, a key player in the global fight against terrorism. The country has rarely seen political changes at the top since gaining independence from France in 1962 after a brutal war.

The UN secretary general, António Guterres, praised what he called “the mature and calm nature in which the Algerian people have been expressing their desire for change”.

Bouteflika’s departure marked a victory for popular protest in the region. But many Algerians’ joy at what some jokingly termed “Bouteflexit” is tempered with concerns over the regime’s efforts to stage-manage the transition period. They hoped Bouteflika’s exit was the first step to removing his entire regime.

“If we use the same mechanisms of power and the same faces, we’ll get the same results – the same system we’ve been fighting against for weeks,” said Habib Brahmia, of the pro-democracy political party Jil Jadid. “Bouteflika is an important face but he isn’t the whole system – we don’t want to create another Bouteflika. We don’t want a monarchy or a military dictatorship, and the Algerian people will continue to be in the streets to show this.”

He said he would like to see a referendum so citizens could vote on the next steps, by nominating figures favourable to the protest movement to lead the transition.

The transitional government is facing a litany of challenges, not least a weakened economy undermined by widespread corruption, and political opposition to its rule. Algerians are expected to take to the streets on Friday once again.

SNATEG, a 600,000-member union of gas and energy workers, vowed to continue a planned three-day general strike from 7 April, to demand a new transitional government, including opposition figures. “The Algerian people do not have confidence in the present government installed by Bouteflika,” said Raouf Mellal, the head of SNATEG.

Questions and fears about how to organise the next step continued to dominate.

Other political figures pushed for unity, fearing division. “The people have now decided no more regionalism,” said prominent human rights lawyer Mustapha Bouchachi in a statement on his Facebook page. “Algeria is open to all of us.”

Adham Youssef contributed reporting from Cairo