Story Highlights• Report of al Qaeda in Iraq leader's death may hint at insurgent rifts
• Analyst: Anbar fighters trying to exclude foreign militants from public role
• Some indigenous Iraqi insurgents say killing civilians is counterproductive
• Regional anti-al Qaeda group has emerged and is working with U.S. forces
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BAGHDAD, Iraq (CNN) -- Reports of fighting between al Qaeda in Iraq and Sunni militants surfaced Tuesday, the latest hints of rising tensions between the two allied groups.
Other reports have emerged this year of tensions between Sunni fighters and the Sunni-dominated al Qaeda in Iraq, particularly from Anbar province, long a favored turf for indigenous Sunni insurgents and foreign fighters infiltrating Iraq from Syria.
The unconfirmed reports from tribal leaders to Iraqi government officials indicate that Abu Ayyub al-Masri, the leader of al Qaeda in Iraq, was killed Tuesday in fighting between al Qaeda militants and Sunni tribal fighters from Abu Ghraib and Falluja. (Watch more about the report of al-Masri's death )
Militant groups in the region "have been trying to put a more Iraqi face" on their movement and have been trying to "exclude the foreign militants from a public role," Bergen said.
Al-Masri is Egyptian and many suicide attacks are carried out under al Qaeda's direction by other foreigners such as Saudis and North Africans.
There has been talk among indigenous Iraqi insurgents that such attacks, which claim civilian lives, are counterproductive.
In addition, Bergen notes that the leader of the Islamic State of Iraq has adopted an alias that reflects his Iraqi roots: Abu Omar al-Baghdadi.
Also, a regional anti-al Qaeda group, the Anbar Salvation Council has emerged which is a coalition touted by the United States and Iraq as a positive development in the war against al Qaeda in Iraq.
Hints of rifts among Sunni-allied insurgents emerged April 12 when two claims of responsibility were announced by Islamic State of Iraq after the deadly attack on Iraqi parliament. (Read more about the attack that claimed eight lives)
While the differing claims used similar and noncontradictory concepts, two claims could indicate differences in the movement, which has about six groups.
Arab media reports hint at rift
More evidence of disunity recently popped up in the Arab media.
Al-Jazeera, the Arabic-language news network, reported last month that Ibrahim al-Shammari, a spokesman for the Islamic Army in Iraq, said his group -- also in the Islamic State of Iraq -- does not plan to work with al Qaeda in Iraq.
Among the reasons, he said, are that al Qaeda has targeted Islamic Army of Iraq members and that their goals are divergent, with the Islamic Army in Iraq being more willing, in some circumstances, to deal with the United States instead of al Qaeda.
Gen. David Petraeus, the top U.S. commander in Iraq, addressed the Sunni backlash against al Qaeda at a news conference last week in Washington.
"Sunni insurgents and the so-called Sunni resistance are still forces that must be reckoned with, as well," Petraeus said. "However, while we continue to battle a number of such groups, we are seeing some others joining Sunni Arab tribes in turning against al Qaeda in Iraq and helping transform Anbar province and other areas from being assessed as lost as little as six months ago to being relatively heartening."
Petraeus said the United States "will continue to engage with Sunni tribal sheikhs and former insurgent leaders to support the newfound opposition of some to al Qaeda, ensuring that their fighters join legitimate Iraqi security force elements to become part of the fight against extremists."
He said it is part of the effort to "reach out to moderate members of all sects and ethnic groups to try to drive a wedge between the irreconcilables and the reconcilables, and help the latter become part of the solution instead of part of the problem."
U.S. working with Salvation Council
CNN's Michael Ware reported in March that the United States is giving local Sunni leaders from the Anbar Salvation Council free rein as long as the insurgents in the group root out and kill al Qaeda.
One Iraqi villager, Abu Miriam, told CNN that locals have tired of al Qaeda. He says his people began fighting U.S. forces, but foreigners infiltrated their ranks.
"If you talk against them, they let you go at first, then come back and behead you later," he said.
Asked what would become of him if al Qaeda knew he was talking, Abu Miriam replied, "I will be killed. In fact, slaughtered, slaughtered with a knife."
These tensions provoke the tribes' Salvation Council to work alongside U.S. Marines and soldiers. Its members carry weapons, launch operations against targets they select, make arrests and conduct interrogations.
"The tribes effectively sought out and killed on a repeated basis elements infiltrating from Syria as well as local elements trying to re-establish," a U.S. official said.
Asked if there had been an assassination program backed by U.S. forces, Zalmay Khalilzad, then-U.S. ambassador to Iraq, said, "We lose no sleep over the struggle against al Qaeda and the killing of al Qaeda people."
The Salvation Council says the United States has given it rifle ammunition, a claim the U.S. military does not dispute, and the Iraqi government has provided 30 vehicles.
"We are not looking for bloodshed. We minimize it," a senior Salvation Council member says. "If a suspect is peaceful, we arrest and hand him to the authorities, but if he resists, there will be no other way than to shoot him."
Al Qaeda has hit back hard at the tribes in recent weeks, sending chlorine bombs, car bombs and suicide bombers in explosive chest vests against their leaders.
CNN's Jomana Karadsheh and Michael Ware contributed to this report.
The leader of al Qaeda in Iraq, Abu Ayyub al-Masri, appears in a video in which he explained how to make bombs.