Hundreds of thousands of people have taken to the streets in Algeria as popular resistance grows to the president’s decision to stand for a fifth term.

Crowds gathered in Algiers throughout the morning despite train services being stopped by authorities, and huge numbers demonstrated in every other major city and most towns. Some chanted slogans calling for a “free and democratic Algeria” and shouted “peaceful, peaceful”.

The protests were the biggest in a series staged almost daily since a huge rally on 22 February. So far all have been without violence. They are the largest demonstration of public discontent in Algeria for many decades, with some observers estimating that millions have taken part.

Social media pages told marchers to come equipped only with “love, faith, Algerian flags and roses”.

On Thursday Abdelaziz Bouteflika, the 82-year-old president who has been in power since 1999, praised demonstrators for their discipline but warned them of unidentified actors who might try to infiltrate their ranks to spread discord and chaos.

The protests have mobilised a wide range of people from all backgrounds. Most of those involved are young but they have received support from journalists, lawyers, unions and the influential association of veterans of the war of independence against the French between 1954 and 1962.

Unusually, one of the most popular imams in Algiers did not pray for the president on Friday and only wished the best for Algeria and its people.

There is widespread resentment in Algeria at the incompetence and corruption of the Front de Liberation 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 is rarely seen in public and has used a wheelchair since a stroke in 2013. He is in Geneva for medical treatment and it is unclear when he will return.

Facebook Twitter Pinterest Algerian lawyers stage a protest march in the capital against Abdelaziz Bouteflika standing for a fifth term. Photograph: Anadolu Agency/Getty Images

Hamza Zait, a journalist and political scientist who spoke to the Guardian from central Algiers on Friday afternoon, said: “We’ve been out here since 9am. People have been chanting ‘no to a fifth term’ without stopping for a second since then.”

Protesters held signs reading: “Dictatorship means shutting your mouth. Democracy means always talking.”

Women have been playing a prominent role in the protests. “It’s really important for women to be out in the streets today in order to show how we feel about Algeria, the government and the constitution,” said Marwa Saïdi, 21, a student who was among the demonstrators in Algiers. “We want to show we will participate in the changes that will happen.”

She added: “We can no longer believe Bouteflika, even if we did before … We have to think more about young people. Algeria deserves better.”

Hasna Badaoui, a 22-year-old student, said she was happy to see so many women among the protesters. “It shows we’re breaking the glass ceiling, really changing things … I want people to hear the voices of women and to take women seriously. I want people to know we’re about more than cooking and housework,” she said.

More than two-thirds of Algerians are under 30. Unemployment is soaring and there is an acute shortage of housing. Authorities have previously relied on social spending and subsidies funded by the country’s oil revenues to quell unrest. However, declining production and lower international oil prices have significantly reduced state revenues.

The opposition group Mouwatana has pressed for the election scheduled for 18 April to be cancelled, and it has called for a general strike.

In the 1990s the cancellation of an election that Islamists had looked set to win triggered a civil war in which at least 150,000 people died. Memories of the violence made many Algerians reluctant to risk political upheaval, but a new generation has reached political maturity.

Andrew Lebovich, an analyst at the European Council on Foreign Relations, said: “The protests can’t be ignored forever but I don’t think they can be crushed ether. I suspect the government is very hesitant to use greater repressive violence and now there are so many people on the streets from such a broad swath of society I think that would be really very difficult.”

Politics in Algeria are notoriously opaque but analysts say there may be divisions among the top FLN officials, spies, businesspeople and Bouteflika’s inner circle who collectively constitute the ruling elite.

His candidacy went ahead because none of the various factions could agree on an alternative, according to a western diplomat recently returned from Algeria.

Lebovich said: “It is very difficult to tell but it seems that there have been some high-level defections. There are cracks in the system that are getting more and more visible and closer and closer to the overlapping circles of people around the president.”