Saudi Grand Mufti Sheikh Abdul Aziz al-Sheikh on Tuesday blasted al-Qaida and Islamic State jihadists as "enemy number one" of Islam, in a statement issued in Riyadh.

"The ideas of extremism, radicalism and terrorism... have nothing to do with Islam and (their proponents) are the enemy number one of Islam," the kingdom's top cleric said.

He cited jihadists from the Islamic State, which has declared a "caliphate" straddling large parts of Iraq and Syria, and the global al-Qaida terror network.

"Muslims are the main victims of this extremism, as shown by crimes committed by the so-called Islamic State, al-Qaida and groups linked to them," the mufti said, quoting a verse in the Koran urging the "killing" of people who do deeds harmful to Islam.

His stance reflects the Saudi clerical community's hostility towards IS jihadists, known for their brutality.

The largely Sunni kingdom of Saudi Arabia favours an austere form of Islam. The two holiest places of Islam, Mecca and Medina, are both in Saudi Arabia.

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.

"In the circumstances the Islamic nation is living through, several countries have been destabilized" by extremists, who "divide Muslims" in the name of religion, the mufti said.

He warned: "In Islam, after heresy, dividing Muslims is the greatest crime."

The mufti urged "tolerance, which was at the origin of Islam's growth and longevity."

King Abdullah vowed on June 29: "We will not allow a handful of terrorists, using Islam for personal aims, to terrify Muslims or undermine our country and its inhabitants."