Last Sunday, the jihadists of the Islamic State group declared a caliphate in areas they control in Iraq and Syria and ordered Muslims worldwide to pledge allegiance to their leader Abu Bakr al-Baghdadi, under the name "caliph Ibrahim".
Qatar-based Qaradawi, seen as a spiritual guide of the Muslim Brotherhood in his native Egypt, said in a statement that the declaration "is void under sharia."
We look forward to the coming, as soon as possible, of the caliphate," Qaradawi said, of the form of pan-Muslim government last seen under the Ottoman Empire.
"But the declaration issued by the Islamic State is void under sharia and has dangerous consequences for the Sunnis in Iraq and for the revolt in Syria," he added.
The influential cleric said the declaration and nomination of Baghdadi by a jihadist group "known for its atrocities and radical views" fail to meet strict conditions dictated by sharia.
The title of caliph, he said, can "only be given by the entire Muslim nation" not by a single group.
Since last Sunday, other leading Muslim figures have denounced the announcement by the Islamic State, which was previously known as the Islamic State of Iraq and the Levant.
A caliphate is fundamentally a universal Islamic state ruled by a single leader with both political and religious authority.
Many Sunnis associate the caliphate with a golden age of Islam, but the declaration made by the Islamic State has triggered indignation among those who see it as heresy.
Al-Azhar, the top authority of Sunni Islam, "believes that all those who are today speaking of an Islamic State are terrorists," senior representative Sheikh Abbas Shuman told AFP earlier this week.