Al-Qaeda in the Islamic Maghreb has rejected the declaration of an Islamist Caliphate in Iraq and Syria, saying it had "defects" that jihadist leaders should rectify, SITE Intelligence said Tuesday.

The group, in a message dated July 4, also reiterated allegiance to overall Al-Qaeda chief Ayman al-Zawahiri, whose leadership appears to have been challenged by the recently declared Islamic State, according to the US-based monitoring group.

It said there was still time "to rectify the defect in this announcement".

The Islamic State (IS) has been fighting in Syria and Iraq and on June 29 proclaimed a "caliphate" straddling both countries and headed by Abu Bakr al-Baghdadi, who now calls himself Caliph Ibrahim.

IS fighters spearheaded a devastating military offensive by a coalition of Sunni militant groups that swept through large swathes of northern and western Iraq.

"Why today... do they make such an announcement without the advice of the leaders of the mujahedeen... (whose) efforts to establish the rightly guided Caliphate were proven?" the statement asked.

AQIM urged consultations among the leaders of various Al-Qaeda factions, including Zawahiri and Baghdadi, to "fix the defects inside the one house, away from the media".

"We confirm that we still adhere to our pledge of allegiance to our sheikh and emir, Ayman al-Zawahiri, since it is a sharia- (Islamic law) accorded pledge of allegiance," it said.

Zawahiri in the past ordered Baghdadi to confine the work of his group to Iraq only, and designated its rival Al-Nusra Front as Al-Qaeda's affiliate in Syria.

But Baghdadi has refused to budge.