The statement by Gen Martin Dempsey yesterday, chairman of the Joint Chiefs of Staff, reflected the delicate balance Washington is trying to strike between limiting Iranian influence and allowing Iraqi leaders to determine their own path to defeating the Islamic State.
US officials have said Iraq did not ask the US to provide air support for the Tikrit offensive, even though the US-led military coalition has been conducting airstrikes in much of Iraq since August and has deployed hundreds of US soldiers to try to regenerate an Iraqi army that collapsed last June.
"This is the most overt conduct of Iranian support, in the form of artillery and other things," Dempsey said in response to questions from members of the Senate Armed Services Committee.
"Frankly, it will only be a problem if it results in sectarianism."
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He said that about two-thirds of the force seeking to retake Tikrit is comprised of Iranian-based Shiite militia fighters. Iraqi government troops make up the other third. Tikrit, the hometown of former Iraqi President Saddam Hussein, is a predominantly Sunni city.
Earlier yesterday, the US general overseeing the military coalition fighting in Iraq told a House panel that the campaign has killed more than 8,500 Islamic State fighters since its bombing campaign began in August.
Army Gen Lloyd Austin, the commander of US Central Command, said the Islamic State, which has controlled key parts of northern and western Iraq since last summer, is no longer capable of seizing and holding new territory.
The bombing also has degraded the group's ability to generate revenue by striking oil refineries and crude oil collection sites, particularly in neighbouring Syria.
"The fact is that he can no longer do what he did at the outset, which is to seize and to hold new territory," Austin said.