ISIS-led insurgents are creating an Islamic state out of the vast strips of land they control in Iraq and Syria, the militants have announced.

Its territory will extend from Syria's Aleppo, once the economic heart of the country, to the Diyala province in the east of Iraq.

The Islamic State for Iraq and the Levant (ISIS), which from now is to call itself simply "Islamic State", will strictly adhere to Sharia law and will consider its enclave to be home to all Muslims, Al Jazeera reports citing an audio recording published online.

Abu Bakr al-Baghdadi, who heads the group, will become "Caliph Ibrahim" to be a "leader for Muslims everywhere".

The "caliph" is a ruler generally pretending to represent all Muslims taking part in the Islamic community (the co-called Ummah). It is considered that the last Caliph was also the last Sultan of the Ottoman Empire.

ISIS now demands that Muslims "reject democracy and other garbage from the West," the BBC quotes them as saying in the message.

Meanwhile the conflict between Iraq's armed forces and the ISIS fighters has taken a new turn as Israel has called for the establishment of a Kurdish state in northern Iraq, where Kurds have been enjoying boosted autonomy.

"We should... support the Kurdish aspiration for independence... [Kurds are] a nation of fighters [who] have proved political commitment and are worthy of independence," Israeli Prime Minister Benjamin Netanyahu was quoted by the Guardian as saying.

Kurds have also managed to take control of Kirkuk, a long Kurdish goal, after the army fled earlier in June due to a wave of Islamist militants who flocked to the city.

The US and other countries are seeking to press Iraq's Prime Minister Nouri Al-Maliki into forging a government of national unity to wind down tensions between Shia, Sunni and Kurdish citizens, after the Shia's dominance in power pushed many Sunnis to join the rebels in their offensive.

ISIS is also targeting the Iraqi capital Baghdad, which it wants to include in its Caliphate.

Iraqi soldiers have been trying to drive away insurgents, and the country's Air Force has carried out air strikes on ISIS targets.