The 68-year-old Abdelaziz, who died on Tuesday, spent more than 40 years fighting for independence for the territory, and was buried in part of the Western Sahara not controlled by Morocco.
A detachment of Polisario fighters presented arms to their former leader whose coffin was draped with the flag of the Sahrawi Arab Democratic Republic, which the movement proclaimed in 1976.
Abdelaziz had been secretary general of the group for most of its decades-long struggle to win independence for the former Spanish colony, but succumbed to a "long illness" on Tuesday.
Algeria is the Polisario Front's main backer, and Prime Minister Abdelmalek Sellal was among those who paid tribute to Abdelaziz in Tindouf.
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Algerian President Abdelaziz Bouteflika decreed eight days of mourning after the independence leader's death.
Abdelaziz had led the Polisario since 1976, three years after the group was founded to struggle for independence for the territory, which Morocco annexed in 1975.
Local Sahrawi people are campaigning for the right to self-determination, but Morocco considers the territory to be part of the kingdom and insists its sovereignty cannot be challenged.