Mohamed Abdelaziz, 68, was secretary-general of the Polisario Front, which fights for an end to Moroccan rule in Western Sahara, a former Spanish colony annexed by Rabat in 1975.
The front has declared 40 days of mourning after which it said a new secretary-general will be chosen.
The UN has long been trying to broker a settlement for the region's future.
However, the conflict is currently deadlocked over a dispute about a referendum on self-determination.
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Algerian President Abdelaziz Bouteflika declared a week of mourning for the Polisario leader, who died in hospital in Algeria after leading the group based in the southern Algerian city of Tindouf for almost 40 years.
Morocco considers Western Sahara to be its "southern provinces", but Algeria and other countries recognise the Saharan Arab Democratic Republic (SADR) declared by the Polisario Front in 1976.
Morocco is the only African country not to be a member of the African Union, of which the SADR is a full AU member.
The Moroccan government has proposed wide-ranging autonomy for the region, but the Polisario Front wants self-determination through a referendum for the local population, as called for in UN resolutions.
In April Morocco expelled  84 UN civilian staff after after UN Secretary General Ban Ki-moon referred to Morocco's rule over Western Sahara as "occupation" during a visit to refugee camps in Tindouf.
The same month, senior Polisario Front member Bachir Mustafa Sayed warned of possible war over the disputed territory if the UN failed to set a timetable for a referendum on self-determination.
The leader of the Western Sahara independence movement has died after a long illness.