Algerian police fired tear gas to disperse hundreds of demonstrators on a third straight day of rare political protests against plans for rarely seen President Abdelaziz Bouteflika to extend his 20-year rule by seeking a fifth term.

Thousands have taken to the streets of the capital Algiers and other cities since Friday, calling on the authorities to abandon plans for the 81-year old Mr Bouteflika to stand in a presidential election on April 18.

Mr Bouteflika, in office since 1999, suffered a stroke in 2013 and has since been seen in public only a handful of times. He has not given a public speech in years.

His opponents say there is no evidence he is in fit health to lead the country, which they say is being ruled in his name by advisers. The authorities say he still has a firm grip on affairs despite the rarity of his appearances.

"People do not want Bouteflika," the crowd chanted at a protest called by an opposition group, Mouwatana.

Journalists working for state media protested against what they said were orders from managers not to cover the marches.

Demonstrators gather during a protest to denounce President Abdelaziz Bouteflika's bid for a fifth term, in Algiers. AP

"The decision of our hierarchy to ignore the big protests shows the hell of our situation," said a statement released by journalists working for state radio.

"I categorically refuse to endorse a behaviour that doesn't respect the most elementary rules of our job," Meriem Abdou, a reporter and editor for state radio, said when announcing that she had decided to quit.

French-Algerians also gathered for rallies in Republic square in Paris.

Protesters from the Franco-Algerian community gather at Republic square to protest against the fifth term of Algerian President, Abdelaziz Bouteflika, in Paris, France. EPA

Since the ruling FLN party picked Mr Bouteflika as its presidential candidate, several parties, trade unions and business organisations have already said they would back him. A weak and divided opposition faces high hurdles in mounting an electoral challenge.

Mr Bouteflika has not directly addressed the protests, but authorities announced this week that he would be travelling to Geneva for unspecified medical checks. There has been no official confirmation he has left the country.

State media quoted a letter written by Mr Bouteflika that was read out at a government oil and gas industry event in the southern town of Adrar, saying: "Continuity is the best option for Algeria".

FLN leader Moad Bouchareb dismissed the protests.

"To those who are dreaming of change, I say 'Have nice dreams,'" he said in televised comments in the western city of Oran on Saturday.

Supporters of Mr Bouteflika have emphasised the risk of unrest. Algerians have bitter memories of a decade of civil war in the 1990s in which 200,000 people were killed. The war was triggered after the army cancelled an election that Islamists were poised to win in 1991.

"Do you want Algeria to go back to years of tears and blood?" said the leader of the powerful UGTA labour union, Abdelmadjid Sidi Said.

A total of 41 protesters were detained on Friday, state news agency APS said. It gave no details of any arrest for the past two days.

Strikes and protests over social and economic grievances are frequent in Algeria, but have generally been localised, rather than touching on national politics.

There was major street unrest in Algeria during the 2011 Arab uprisings that brought down the rulers of North African neighbours Egypt, Libya and Tunisia. But Algerian security forces managed to contain it without Mr Bouteflika's grip on power loosening. The government also announced reform and subsidy packages to ease the tension.

But lower oil prices in recent years have hurt the country’s economy, reigniting discontent. More than a quarter of Algerians under the age of 30 are unemployed, according to official figures, and many feel disconnected from an elite made up of veteran fighters from Algeria's 1954-62 independence war with France.

Throughout the 2000s, Mr Bouteflika’s government embarked on an ambitious investment drive to build the economy off the back of the country's large oil and gas revenue and mineral resources. However, after 20 years in power and with a country still heavily reliant on natural resources, many have accused the government of corruption, nepotism and failing to ensure the boom years improved the lives of ordinary people.

However, with no clear successors to Mr Bouteflika, the country’s leaders see few viable options for a new administration.