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The move is an expansion of the group's ambitions to wage a holy war and posed a direct challenge to the central leadership of al Qaeda, which has already disowned it.
The group, previously known as the Islamic State in Iraq and the Levant (ISIL), also known as ISIS, has renamed itself "Islamic State" and proclaimed its leader Abu Bakr al-Baghadi as "Caliph" - the head of the state, the statement said.
"He is the imam and khalifah (Caliph) for the Muslims everywhere," the group's spokesman Abu Muhammad al-Adnani said in the statement, which was translated into several languages and an Arabic audio speech.
"Accordingly, the "Iraq and Sham" (Levant) in the name of the Islamic State is henceforth removed from all official deliberations and communications, and the official name is the Islamic State from the date of this declaration," he said.
Charles Lister, Visiting Fellow at the Brookings Doha Cnter, saw considerable significance in the move.
"Whatever judgments are made in terms of its legitimacy, (the) announcement that it has restored the Caliphate is likely the most significant development in international jihadism since 9/11.
"The impact of this announcement will be global as al-Qaeda affiliates and independent jihadist groups must now definitively choose to support and join the Islamic State or to oppose it."
Fighters from the group overran the Iraqi city of Mosul last month and have advanced towards Baghdad. In Syria they have captured territory in the north and east, along the frontier with Iraq.
"It is incumbent upon all Muslims to pledge allegiance to (him) and support him...The legality of all emirates, groups, states, and organizations, becomes null by the expansion of the khalifah's authority and arrival of its troops to their areas," the statement said.