Some 30,000 men have been involved in a week-old operation to recapture Tikrit, one of the jihadists' main hubs since they overran large parts of Iraq nine months ago.
But in a sign of the brutal lengths to which IS will go to maintain control, the group executed 20 men in Iraq's northern province of Kirkuk and strung up more than a dozen of their victims' bodies in public.
General Martin Dempsey's visit also coincided with the start of an offensive by Kurdish peshmerga forces in Kirkuk that further increases the pressure on the last IS strongholds east of the Tigris river.
The United States began carrying out air strikes against IS in August, the first of what is now a 60-nation coalition of mostly Western and Arab states supporting Baghdad's fightback.
Dempsey emphasised that strikes must "be very precise" to avoid "additional suffering," also saying that while the priority has been protecting people, it may also be possible to use air power to defend Iraqi heritage sites being targeted by the jihadists.
During a visit to a French aircraft carrier in the Gulf taking part in the air campaign, Dempsey appealed for "strategic patience" in the fight against the IS group in Iraq and Syria.
"Carpet bombing through Iraq is not the answer," he said yesterday.
Dempsey stressed that training the Iraqi army, which imploded when IS attacked in June 2014, would take more time, as would initiatives to bring Iraq's Sunni Arab minority back into the fold.
Iraqi soldiers, police and the increasingly influential paramilitary Popular Mobilisation units, which are dominated by Shiite militias, have been closing in on Tikrit in recent days.
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