The coalition ally of Algeria’s ruling party has called for the country’s ailing president to resign, piling pressure on Abdelaziz Bouteflika after the army chief also demanded he be declared unfit for office.

In a statement signed by its leader, recently sacked prime minister Ahmed Ouyahia, the National Rally for Democracy (RND) on Wednesday said it “recommends the resignation of the president... with the aim of smoothing the period of transition.”

The army chief, Lt Gen Ahmed Gaid Salah, said in a televised address on Tuesday that the time had come to trigger a constitutional process to remove the president. Popular protests calling for Bouteflika to go have held in Algeria for more than a month.

“It is necessary, even imperative, to adopt a solution to get out of this crisis that responds to the legitimate demands of the Algerian people, and which respects and adheres to the constitution and safeguards the sovereignty of the state,” Lt Gen Salah said.

Article 102 of Algeria’s constitution allows the constitutional council to declare the presidency vacant if the incumbent is too ill to exercise his functions, then ask parliament to declare him unfit. The leader of the upper house would then take over in a caretaker capacity for 45 days.

The article should be invoked as “the only guarantee of preserving a stable political situation”, Salah said.

Bouteflika, 82, uses a wheelchair and has rarely been seen in public since suffering a debilitating stroke in 2013. The president reversed an earlier decision and agreed on 11 March not to stand for a fifth term in elections that were due in April, but have now been postponed.

He stopped short of standing down as head of state, however, saying he intended to stay on until a new constitution was adopted. Demonstrators suspect he is simply trying to cling on after 20 years in power and have been taking to the streets in their hundreds of thousands for the past five weeks.

“This solution achieves consensus and must be accepted by all,” Salah, who is also the deputy defence minister, said. The army chief is one of Algeria’s top power-brokers and Salah is viewed as a key Bouteflika loyalist and influential member of Algeria’s ruling elite.

His announcement potentially clears the way for elections to be organised in the coming months unless the president, who has often flown to France or Switzerland for treatment, recovers.

Salah’s announcement came two days after the country’s ruling National Liberation Front (FLN) withdrew its support for Bouteflika’s suggestion that a “national dialogue conference” should be held in a bid to haul the country out of its political deadlock.

A party spokesman, Hocine Khaldoun, said on Sunday that the conference, involving opposition parties and civil society and aimed at reforming the country’s constitution, would not solve the problem. “What we need is an elected president,” he said.

A veteran of Algeria’s independence struggle against France, Bouteflika is credited with helping to end the country’s decade-long civil war between government forces and Islamist militants, in which an estimated 200,000 people died, in 2002.

Many Algerians have since tolerated a restrictive political regime and omnipresent state security service in exchange for relative calm and stability. The scale of the past month’s protests took many observers by surprise.

The army chief’s announcement was welcomed with joy on the streets of Algiers, where hundreds of students were protesting again on Tuesday. “Algerian leaders think we will give up … Of course not. We will be back here every Tuesday until they all leave,” said Sayet, 24, an architecture student.