ISIS (the Islamic State in Iraq and the Levant) also proclaimed the group’s leader, Abu Bakr al-Baghdadi, as caliph and “leader for Muslims everywhere”.
Setting up a caliphate ruled by the strict Islamic law has long been a goal of many jihadists.
Meanwhile, Iraq’s army continued an offensive to retake the northern city of Tikrit from the ISIS-led rebels.
Tikrit was seized by the insurgents on June 11 as they swept across large parts of northern-western Iraq.
In a separate development, Israel called for the creation of an independent Kurdish state in response to the gain made by the Sunni rebels in Iraq.
ISIS announced the establishment of the caliphate in an audio recording posted on the internet.
The group also said that from now on it would be known simply as “the Islamic State”.
The declaration harks back to the rise of Islam, when the Prophet Muhammad’s followers conquered vast territories in the Middle Ages.
The Sunni-Shia split happened because of a dispute over the succession to Muhammad, with the Sunnis following caliphs as their religious authority.
ISIS said the Islamic state would extend from Aleppo in northern Syria to Diyala province in eastern Iraq.
Abu Bakr al-Baghdadi would become the leader of the state and would be known as “Caliph Ibrahim”.
In the recording, the rebels also demanded that all Muslims “pledge allegiance” to the new ruler and “reject democracy and other garbage from the West”.
On Sunday, Iraqi government jets struck at rebel positions and clashes broke out in various parts of Tikrit, witnesses and officials said.
Troops had reportedly pulled back to the nearby town of Dijla as Saturday’s initial offensive met stiff resistance.
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