The Kurds would remain autonomous in their northern redoubt, retaining control over their peshmerga militias.
He has issued a decree disbanding militias, though letting the Kurdish regional government keep its own peshmerga force.
Iraqi forces were "rapidly collapsing" in the face of the Peshmerga-Special Forces advance, CNN reporters said from the region.
They have agreed to let the Kurds' peshmerga (former guerrilla) fighters continue to serve as police in the north.
Most of Iraq's private armies will take part, including the 75, 000 Kurdish peshmerga fighters and the 15, 000 Shia militiamen from the Badr Organisation.
Reports from the border area say the Kurdish peshmerga patrolling the Syrian border are sometimes just a few hundred yards from regular Iraqi troops.
CNN: Kurds' ambitions add explosive element to Syria equation
The United States has relied on the Kurds to maintain peace in their areas, and to supply the Iraqi army with members of their militia, known as the Peshmerga.
He looks just like his pictures, the red and white scarf neatly tied on his head, the traditional peshmerga outfit cinched in at the waist by a wide belt.
The Peshmerga, backed by U.S. Special Forces, pushed into Kirkuk after a steady northern campaign that saw the Kurds take over nearly 300 villages following a near-constant bombing campaign by coalition aircraft.
Now about six small teams of US special forces have moved into the city centre and some regular peshmerga units been moved in to protect public properties, put up checkpoints and curb the looting.
In the north, Kurdish leaders have refused to disband their peshmerga fighting forces, forcing Mr Allawi to backtrack on his demand that all militias be incorporated into the re-formed Iraqi security forces or return to civilian life.
In another sign of how difficult it will be to disband militias or fold them into government forces, Mr Talabani, the Kurdish president, said that Kurdish peshmerga forces in the north were not militias, but rather organised forces.
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