France has officially acknowledged for the first time that it carried out systematic torture during Algeria’s independence war – a landmark admission about conduct in the conflict which ended 56 years ago and that has been shrouded in secrecy and denials.

The president, Emmanuel Macron, said France instigated a “system” that led to torture during the Algeria conflict, and the past must now be faced with “courage and lucidity”.

Macron used the case of the mathematician Maurice Audin, a Communist pro-independence activist who disappeared in 1957, to make a far-reaching comment about France’s sanctioning of torture, going further than any previous president.

The Elysée said Macron would acknowledge in a letter to be presented to Audin’s widow and family on Thursday afternoon that Audin “died under torture stemming from the system instigated while Algeria was part of France”.

Macron’s office said he would detail a system of arrest and detention legally put in place by parliament and decree in the late 1950s that allowed forces to hold and interrogate suspects, leading to “acts that were sometimes terrible, including torture.”

Macron will announce that archives will be fully opened up to historians, families and organisations seeking the truth about the large number of disappeared civilians and soldiers, both French and Algerian, whose bodies have never been found.

During the 1954-62 war, which claimed 1.5 million Algerian lives, French forces brutally cracked down on independence fighters in the then colony, which was ruled by Paris for 130 years.

The French state has never previously admitted that its military forces routinely used torture. During the war the government censored newspapers, books and films that claimed it had used torture, and after the war the atrocities committed by its troops remained a taboo subject in French society.

Sylvie Thenault, a historian, said the French state’s acknowledgement that Audin’s death resulted from a “system” pointed to a broader recognition of wrongdoing.

Another historian, Raphaëlle Branche, told Le Monde: “It will no longer be possible to deny the systematic nature of torture in Algeria.”

Benjamin Stora, an expert on Algeria and the head of France’s museum of the history of immigration, who has advised Macron on the issue, said: “This declaration will leave an indelible mark.”

He wrote in Le Monde: “Are we, at last, coming out of this kind of amnesia over a war that was for so long never named?”

Macron’s statement was seen as the latest important official French recognition of 20th-century events.

The most significant move by France to face its history came in 1995 when the then president, Jacques Chirac, acknowledged that France as a whole was responsible for the roundup of 76,000 Jews sent to Nazi death camps during the second world war.

Chirac’s statement that the “criminal folly” of the German occupation was “assisted by the French people, by the French state” lifted the last taboo of the occupation and the collaborationist Vichy regime. He apology was the first time a postwar French head of state had fully acknowledged France’s role.

Macron is the first French president born after the Algeria conflict. He sparked controversy on the presidential campaign trail last year by declaring that France’s colonisation of Algeria was a “crime against humanity”.

He later backtracked on his comments, calling for “neither denial nor repentance” over France’s colonial history and adding: “We cannot remain trapped in the past.”

Audin’s family have for years been seeking the truth over his disappearance. An assistant professor at the University of Algiers, Audin was 25 when he was arrested at his home by French paratroopers and accused of harbouring armed members of the Algerian Communist party. He was tortured repeatedly in a villa in the Algiers neighbourhood of El Biar.

His widow, Josette, was told 10 days later that the mathematician had escaped while being transferred between jails. This remained the official version of events until 2014, when Macron’s predecessor Francois Hollande acknowledged that Audin died in detention.

• This article was amended on 18 September 2018. An earlier version referred to the “60-year-old conflict”. The war ended 56 years ago, in 1962.