Turkey says it has the right to use force to combat the PKK, which uses the semi-autonomous Kurdish region of northern Iraq as a launch pad for attacks in which they have killed dozens of Turkish soldiers in recent months.
The US, which lists the PKK as a terrorist group, says it shares common interests with Turkey in stopping PKK activities in Iraq, but fears an escalation in tension could destabilise Iraq's northern region.
Ryan Crocker, the US ambassador to Iraq, said: "We all have a pretty substantial interest in stability inside Iraq.
"I think none of us ... wants to see the operations persist in a manner that can threaten stability inside Iraq."
Turkey has 100,000 troops on the border with Iraq. It has not carried out a full-scale invasion, but launches limited ground incursions and air strikes.
Iraqi officials said that Turkish fighter jets had carried out an assault on Saturday in which no one was hurt.
Turkey, a member of Nato, has increased its attacks on the PKK in Iraq over the past week, launching two offensives, one involving 50 fighter jets on December 16 and the other involving several hundred ground troops two days later.
The Turkish military said hundreds of PKK fighters were killed in the recent operations. Ankara says the PKK has killed nearly 40,000 people since it began an armed struggle for a separate Kurdish homeland in 1984.
Turkey says 3,000 PKK fighters are based in camps in northern Iraq.