Hundreds of students protested in the Algerian capital on Tuesday, accusing ailing President Abdelaziz Bouteflika of seeking to prolong his two-decade rule despite abandoning his bid for a fifth term.

"The students are resisting the extension of the fourth mandate," they chanted in a square outside the main post office of Algiers, a day after Bouteflika cancelled next month's presidential election.

Half a dozen police vans were parked around the Place de la Grande Poste, which has been the epicentre of protests demanding the 82-year-old leader step down.

"No tricks, Bouteflika," the demonstrators chanted.

They were responding to calls on social media for renewed mass protests, after the cancellation of the April presidential polls raised fears of a ploy to extend Bouteflika's hold on power.

"We will march more determined than ever to end this system, to end this mafia. We want a republican and democratic state," one message calling for demonstrations said.

"No to manipulation, let's be vigilant. The battle is not won. Those in power want to stay and proof of this is that the interior minister has become the prime minister," it said.

On Monday, Bouteflika said in a message carried by the official APS news agency: "There will not be a fifth term" and "there will be no presidential election on April 18".

He said new polls would be held at an unspecified date to be decided by a "national conference" - effectively extending his mandate.

He also named interior minister Noureddine Bedoui as the new prime minister to replace the unpopular Ahmed Ouyahia, APS said.

Bouteflika, who has been rarely seen in public since suffering a stroke in 2013, said he was responding to "a pressing demand that you have been numerous in making to me".

Demonstrations against his re-election bid had brought tens of thousands onto the streets for the past three Fridays, with smaller demonstrations taking place on other days.

There were also calls online for students in the northeastern city of Annaba to protest Tuesday inside and outside university campuses.

Calls were also put out for demonstrations to be held nationwide on Friday.

The influential El Watan newspaper on Tuesday carried a banner headline suggesting that Bouteflika's move to drop his bid for a fifth term was merely a "ploy".

Liberte, another French-language daily, spoke of a "sham" and said that Bouteflika was seeking to deceive the people again.

Former colonial power France cautiously "welcomed" Bouteflika's decision not to stand for re-election.

French President Emmanuel Macron called however for "a transition in a reasonable timeframe".

"I welcome the decision by President Bouteflika, which is the start of a new page in the development of Algeria's democracy," Macron told a press conference during a visit to Djibouti in east Africa.

"I welcome the dignity with which the population and particularly Algeria's youth, was able to express its hope, its desire for change, as well as the professionalism of the security forces," he added.

But he argued the country needed "a transition in a reasonable timeframe" from Bouteflika's 20-year rule.

The Paris government has been extremely cautious in its statements about Algeria in recent weeks amid concern it could be seen to be intervening in the affairs of its former north African colony.

French policymakers remain concerned about the risk of political instability in the energy-rich country, which has seen more than two weeks of peaceful demonstrations against Bouteflika.