Islamist militant group Isis has said it is establishing a caliphate, or Islamic state, on the territories it controls in Iraq and Syria.
It 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.
The city was seized by the insurgents on 11 June 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 (the Islamic State in Iraq and the Levant) announced the establishment of the caliphate in an audio recording posted on the internet.
Isis also said that from now on it would be known simply as "the Islamic State".
The BBC's Middle East editor, Jeremy Bowen, says 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.
The Isis "Islamic State" challenges the borders established by Britain and France in the 20th Century when the Ottoman Empire collapsed, our correspondent says, adding that Isis militants see themselves as a band of revolutionaries not interested in popular legitimacy.
Isis said the Islamic state would extend from Aleppo in northern Syria to Diyala province in eastern Iraq.
Abu Bakr al-Baghdadi, the group said, 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.
"The security forces are advancing from different areas", Lt-Gen Qassem Atta told journalists. "There are ongoing clashes."
Troops had reportedly pulled back to the nearby town of Dijla as Saturday's initial offensive met stiff resistance.
The heavy fighting over the two days caused many casualties on both sides, eyewitnesses and journalists told the BBC.
Fear inside Tikrit
"We cannot live here another day. The entire night we have only heard bombs bursting all around the hospital" - Marina Jose, one of 46 stranded Indian nurses at a Tikrit teaching hospital, tells BBC
'No-one wants to stay here'
Insurgents were reported to have shot down a helicopter and captured the pilot.
The witnesses said the Iraqi forces had been hampered in their bid to retake Tikrit by the large number of improvised explosive devices laid on the approaches to the city.
Iraq said on Sunday it had received the first batch of military jets ordered from Russia in order to help fight the militants.
Meanwhile, Israeli Prime Minister Benjamin Netanyahu called for the creation of an independent Kurdish state in response to gains made by Sunni insurgents in Iraq.
In a speech in Tel Aviv, he said the Kurds were "a nation of fighters and have proved political commitment and are worthy of independence".
Earlier this week, Iraqi Kurd leader Massoud Barzani told CNN that "the time is here for the Kurdistan people to determine their future".
Correspondents say the Kurds have long held aspirations for an independent state but they remain divided between Syria and Turkey, Iran and Iraq.
The international community, including neighbouring Turkey and the US, remain opposed to the breakup of Iraq.