Iraqi Kurdish fighters and US special forces have captured the entire area held by Islamic radicals in the mountains of northern Iraq near the border with Iran.
The joint operation against the radicals from the Ansar al-Islam group was launched last Friday.
The PUK had long been preparing a ground assault
The group is accused by both the Kurds and the Americans of having links with international terrorism and the al-Qaeda movement.
There are no precise figures yet for the number of the Ansar killed, though a spokesman for the US special forces said it was 300.
Very few prisoners were taken, as the Ansar apparently fought ferociously.
Kurdish leaders from the Patriotic
Union of Kurdistan (PUK) - the group that carried out the bulk of the offensive - believed that at least 300 Ansar elements were still at large and that 150 had slipped across the high mountain ridge on the border with Iran.
US special troops said they would analyse abandoned Ansar materials
They said the Iranians had arrested the Ansar fugitives, and the PUK was asking to have them handed back.
The US special forces gave an unusual news conference in the town of Halabja near the Iranian border.
They said that they had taken away for analysis materials found in a complex abandoned by the Ansar which they believed were related to attempts to develop chemical or biological weapons.
The US special forces were full of praise for the Kurdish peshmerga fighters.
"The peshmerga are the ones that did it," a US special forces soldier said.
"A terrorist organisation that has held grip on this region for the last several years was rooted out and neutralised."
The combination of large numbers of peshmerga, small numbers of US special forces and American air power has been highly successful.
Both parties would now like to apply that same formula to the northern front with the Iraqi army.
That would make the Iraqi Kurds the second biggest troop contributor to the coalition effort, but it would also anger Turkey, which does not want to see the Kurds move forward.