Algerian news agency APS on Sunday quoted an official source as saying that President Butaflika had lifted Algerian entry visa restrictions for Moroccan citizens as "an act of national sovereignty".
The source added that the measure was in response to the similar move announced by King Muhammad VI of Morocco on 30 July 2004.
The news agency said Butaflika had informed King Muhammad of his decision, which it described as a new step towards further rapprochement between the Algerian-Moroccan peoples.
The agency did not say when the decision would be executed.
Morocco has welcomed the Algerian decision, which Moroccan news agency MAP said came days after meetings between Butaflika and King Muhammad in Algiers on the sidelines of the recent Arab League summit.
The Algerian authorities imposed visa entry on Moroccans in 1994 after Morocco closed its land border with Algeria after the killing of a number of Western tourists in a hotel in Marrakech.
The attack was believed to be carried out by Muslim activists, which Rabat said were supported by Algerian intelligence.
Algerian-Moroccan relations have remained tense over the issue of Western Sahara since 1975. Rabat accuses Algiers of supporting the Polisario Front, a group claiming to represent the population of Western Sahara and seeking independence from Morocco.
Algeria, which provides the Polisario with material, financial, and political support and sanctuary in south-western Algeria around Tinduf, contends that the Sahrawis living there have a right to self-determination under the UN charter.