State department spokeswoman Heather Nauert urged all parties to "avoid further clashes".
In a statement on Monday, Ms Nauert said Washington was "very concerned by reports of violence around Kirkuk".
"We support the peaceful exercise of joint administration by the central and regional governments, consistent with the Iraqi constitution, in all disputed areas."
Ms Nauert said the US was working with officials from all parties to "encourage dialogue", warning that "there is still much work to be done to defeat Isis (Islamic State) in Iraq".