But the defence secretary said the offer was conditional on Iraqi forces shaping up after the debacles that has seen them lose large cities such as Mosul, Tikrit and Ramadi.
"We are willing to do more... When and if (the Iraqis) develop capable, motivated forces of their own that can take and retain territory," he said as he met some of the 3,500 US military trainers and advisers in Iraq.
His visit came as Iraqi troops, some of which were trained by the United States, tightened the noose on IS in Ramadi, the capital of Anbar province which the government lost in May.
He also met a number of top Sunni politicians, including officials from the regions most affected by the massive onslaught the extremist Sunni IS launched in June 2014.
Government and allied forces recaptured Tikrit in April but any attempt to take back Mosul, the capital of Nineveh and the largest city in the "caliphate" IS proclaimed over parts of Iraq and Syria last year, has been put on the back burner.
The government has instead focused on Anbar, the vast western province that stretches from the Syrian, Saudi and Jordan borders all the way to the outskirts of Baghdad.
"Iraqi security forces are in the process of encircling" Ramadi, said Pentagon spokesman Colonel Steve Warren, who is travelling with Carter.
He put the number of jihadist fighters defending the city at 1,000 to 2,000.
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