The radical group took control of large swathes of the north and western parts of the country months ago after an offensive and the collapse of Iraqi military units.
Following months of an air campaign by a US-led coalition and a rallying of Iraqi forces, the Islamic State (IS) grip on parts of the country is fading, the Pentagon claims.
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"Iraqi security forces and coalition airpower have unquestionably inflicted some damage on ISIL," he said using another acronym for IS.
The lost territory amounts to some 13,000 to 17,000 square kilometres, Warren said.
A much touted Iraqi offensive has been announced targeting the city of Mosul.
Since August, coalition aircraft have conducted airstrikes on 3,244 IS targets, 1,879 in Iraq and 1,365 in Syria. The US has carried out about 80 per cent of the strikes, according to Pentagon data.
In Syria, IS has maintained its influence on the ground, recently losing areas around Kobane, but gaining ground around Homs and Damascus and in the Yarmuk refugee camp, Warren said.
US President Barack Obama meets today at the White House with Iraqi Prime Minister Haider al-Abadi.
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