He was ambassador to Paris, London, Moscow, Washington and Belgrade, and also held several ministerial portfolios including foreign minister.
Malek was one of the main negotiators during the US hostage crisis in Iran in 1980.
He was a member of the high state committee which governed Algeria from 1992 to 1994 during its civil war against armed Islamists.
He became prime minister in 1993, before founding a political party, the National Republican Alliance, two years later.
He authored several books and advocated for the separation of state and religion.
“Algeria has lost a witness of his era, an enlightened patriot,” former communications minister Abdelaziz Rahabi told AFP. “He was one of those who established the foundations of Algerian diplomacy.”
Malek is to be buried on Sunday at El Alia national cemetery in Algiers.