The fighting erupted yesterday evening between the jihadist Islamic State of Iraq and the Levant (ISIL) and the Army of the Men of the Naqshbandiyah Order (JRTN) in Hawija, in Kirkuk province, said the sources.
There were differing accounts as to what sparked the firefight, which is a potential sign of the fraying of the Sunni insurgent alliance that has overrun vast stretches of territory north of Baghdad in less than two weeks.
One security official said JRTN fighters had refused an ISIL demand to give up their weapons and pledge allegiance to the jihadist force.
Witnesses, however, said the two sides clashed over who would take over multiple fuel tankers in the area.
Analysts have noted that while the Sunni insurgents, who are led by ISIL but also include a litany of other groups including loyalists of now-executed dictator Saddam Hussein, have formed a wide alliance, it is unclear if the broader grouping can hold together given their disparate ideologies.
ISIL espouses an extremist interpretation of Islam and wants to establish an Islamic state, whereas other armed groups have political differences with the regime in Baghdad, suggesting the alliance could eventually break down.
"If history repeats itself, then ISIL, because it's got a transnational goal of a caliphate, because it's radical, because it's got this ludicrously absurd... approach to Islam, they can't help but break that coalition," said Toby Dodge, head of the Middle East Centre at the London School of Economics.
ISIL, which is seen as the most capable militant group in Iraq, has for months clashed with groups opposed to President Bashar al-Assad in neighbouring Syria, where it also operates and where it is seen as far more extremist than even Al-Qaeda's front group in the country.