"This group is aggressive and oppressive. It sheds blood," Al-Eqtisadiah daily quoted Grand Mufti Sheikh Abdul Aziz al-Sheikh as saying.
"If they fight Muslims, then Muslims must fight them to rid people and religion of their evil and harm," he said in a response to a request from an Iraqi for a fatwa or edict on fighting IS.
"They have been killing ever since they began their fight. Their killing is filled with mutilations and hideousness that distort (the image of) Muslims," Sheikh said.
The United States last month launched air strikes against the militant group in Iraq, in support of government forces and allied tribesmen, as well as Kurdish peshmerga fighters in the north.
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Last month, the desert kingdom's highest religious authority branded Al-Qaeda and IS jihadists Islam's "number one enemy", and warned Muslim youths to steer clear of "calls for jihad" issued on "perverted" grounds.
IS jihadists, already well established in Syria, launched an offensive in Iraq on June 9 and rapidly seized control of vast swathes of Sunni territory there.
The ultra-conservative and largely Sunni monarchy of Saudi Arabia is the home of Islam's holiest places, Mecca and Medina.