Beirut (AFP) - A jihadist group in Syria has publicly executed and crucified nine men, eight of them rebels fighting both President Bashar al-Assad's regime and the jihadists, a monitor said on Sunday.

The report comes amid fierce clashes on the outskirts of Damascus between the Islamic State of Iraq and the Levant, which is spearheading a major offensive in Iraq, and rebels, the Syrian Observatory for Human Rights said.

"ISIL executed eight men in Deir Hafer in the east of Aleppo province" on Saturday because they belonged to rebel groups that had fought against the jihadists as well as Assad's forces, it said.

ISIL then "crucified them in the main square of the village, where their bodies will remain for three days", the Britain-based monitor said.

Also in Aleppo province, a ninth man was executed and crucified in Al-Bab town near the border with Turkey.

ISIL first emerged in Syria's war in late spring last year and was initially welcomed by some Syrian rebels who believed its combat experience would help topple Assad.

But subsequent jihadist abuses quickly turned the Syrian opposition, including Islamists, against ISIL.

Rebels launched a major anti-ISIL offensive in January 2014, and have pushed them out of large swathes of Aleppo province and all of Idlib in the northwest.

However, ISIL remains firmly rooted in Raqa, its northern Syrian headquarters, and wields significant power in Deir Ezzor in the east near the border with Iraq.

Activists say the group's Iraq offensive and capture of heavy weapons -- some of them US-made -- appears to have boosted its confidence in Syria.

East of Damascus, "fierce clashes broke out early Sunday between rebels from the Army of Islam and ISIL near the town of Hammuriyeh", the Observatory said.

The Army of Islam is a major component of the Islamic Front, Syria's largest rebel coalition which has been fighting ISIL for months, but such fighting in Damascus province is unprecedented.

Regime soldiers and warplanes backed by Lebanon's Shiite Hezbollah also pounded rebel positions near the capital with rockets and surface-to-surface missiles, said the Local Coordination Committees activist network.

Syria's war began as a peaceful protest movement in March 2011 demanding political change, but became an armed insurgency when Assad's regime unleashed a brutal crackdown.

Many months into the fighting, jihadists began to flock to Syria where upwards of 162,000 people have been killed and millions displaced in more than three years of conflict.