Algerian freedom fighter Ali Boumendjel was "tortured and murdered" by French troops, French President Emmanuel Macron said.
Mr Macron made the admission "in the name of France" during a meeting with Boumendjel's grandchildren.
Mr Macron angered Algerians last year after refusing to apologise for atrocities committed during Algeria's 1954-1962 war of independence.
But Mr Macron did agree to form a truth commission to investigate French actions and his admission to the Boumendjel family appears to be in line with that goal.
Boumendjel, a nationalist and lawyer, was arrested during the battle of Algiers by the French army, "placed incommunicado, tortured, and then killed on 23 March 1957", the Elysee Palace said.
"Ali Boumendjel did not commit suicide. He was tortured and then killed," Mr Macron told Boumendjel's grandchildren, according to the palace statement.
It is not the first time French authorities admitted the country's role in his death but it is the first time the country's most powerful figure has become involved, and comes as France is being recommended to officially recognise what happened.
In 2000, Paul Aussaresses, the former head of French intelligence in Algiers, confessed to ordering Boumendjel's death and disguising the murder as suicide.
"Paul Aussaresses himself confessed to having ordered one of his subordinates to kill him and to disguise the crime as suicide," the statement said.
The Elysee Palace said that Mr Macron repeated his desire to give families the opportunity to find out the truth about this chapter of history.
Mr Macron told the Boumendjel family he wanted to "look history in the face" and collect testimonies from people who suffered in the war.
"It is in this spirit that the president of the republic wished to make this gesture of recognition, which is not an isolated act," the statement said.
"No crime, no atrocity committed by anyone during the Algerian War can be excused or concealed. They must be looked at with courage and lucidity, with absolute respect for all those whose lives [they have] shattered [and whose] destiny they have torn apart."
Historian Benjamin Stora's report for the French government submitted on January 20 recommended that France officially recognise the assassination.
Last month, Boumendjel's niece, Fadela Boumendjel-Chitour, denounced what she called the devastating lie France had told about her uncle.
During his 2017 election campaign, Mr Macron said the occupation of Algeria was a "crime against humanity".
He has since said there was "no question of showing repentance" or of "presenting an apology" for abuses committed in the North African country.