The group said it had dealt with al-Qaeda with "patience and wisdom" to keep a united "resistance front".
"But this was not fruitful," the group said.
The growing tension highlights a struggle for power involving Sunni tribal leaders who are angered by al-Qaeda in Iraq's indiscriminate killing of civilians.
Sunni Arab officials have also urged what they call "the real resistance" to disown al-Qaeda and engage in talks with the government to end violence which has driven the country closer to an all-out civil war.
"We also call ... on every Qaeda member in the Land of Mesopotamia to review themselves and their positions ... and for those who committed wrongful acts to repent quickly," the statement said.
Also on Friday, Nuri al-Maliki, the Iraqi prime minister, ordered that jobs and pensions be offered to former officers, many of whom had joined armed Sunni groups such as the Islamic Army of Iraq.
The Islamic Army in Iraq's appeal to al-Qaeda comes against a backdrop of continued violence in Sunni Arab areas.
On Friday, at least 27 people were killed by a chlorine truck bomb in the city of Ramadi, west of Baghdad.
The suicide attack was the latest in a series involving the poisonous chemical.
Poice said the target was a police station but the bomber blew himself up 200 metres away from it, near a residential area and market.
"The truck contained many tonnes of chlorine and TNT which were covered by sacks full of fertilisers," a local police officer said.
Meanwhile, in the city of Diwaniya, Iraqi and US forces clashed on Friday with fighters loyal to Moqtada al-Sadr, the Shia leader, in a major operation.
The US military said in a statement that Operation Black Eagle aimed "to disrupt militia activity and return security and stability of the volatile city back to the Iraqi government".
Residents and an Iraqi security source in Diwaniya said a curfew had been imposed and that troops were blocking streets and conducting house-to-house searches.
The security source said police in the city, many of whom are suspected of being infiltrated by Sadr's Mahdi Army militia, had been ordered to stay at home.