Kurdish rebels have killed 15 soldiers in separate attacks in the past two days.
There is increasing anger in the country over the rebels' ability to find refuge in neighbouring Iraq. Shelling claims
The military said on Sunday it had shelled an area near Iraq to try to stop PKK members from escaping across the border after an attack in the southeast province of Sirnak that killed 13 soldiers.
However, residents in northern Iraq claim the Turkish shelling is landing well within their territory. Kurdish farmers displayed craters on Tuesday they said were left by artillery shells that hit close to the border.
|"I am not sure that unilateral incursions are the way to go, the way to resolve the issue"|
Sean McCormack, US state department
Ankara has not confirmed any shelling of Iraqi territory.
Local officials in the Iraqi Kurdish-run northern region, feared the shelling was a sign of more to come.
In the city of Arbil, 350km north of Baghdad, the Kurdish governor warned Turkey on Tuesday that its troops would sustain heavy losses if they began operations in the region.
Nozad Hadi, the region's governor, said: "If the Turkish troops decided to enter into the Iraq's Kurdistan territories, their decision would be wrong and they would sustain heavy casualties and material losses."
Turkey's parliament would have to authorise any large-scale military operation into Iraq, but troops could pursue rebels over the border in smaller, so-called "hot pursuit" operations without such authorisation.
Ankara has long claimed the right to stage such limited operations under international law as legitimate self-defence and claims about 3,000 PKK fighters are currently in northern Iraq.
Turkey blames the PKK for the deaths of more than 30,000 people since the group began its armed campaign for a homeland in the southeast of the country in 1984. Public pressure
The US said it supported Turkey and Iraq in their efforts to combat the PKK but warned against military incursions from Ankara.
"If they have a problem, they need to work together to resolve it and I am not sure that unilateral incursions are the way to go, the way to resolve the issue," Sean McCormack, a spokesman for the US state department, said on Tuesday.
Asked whether Washington had urged restraint on both sides, McCormack said sovereign states had to make their own decisions about how best to defend themselves.
"We have counselled both in public and private for many, many months the idea that it is important to work cooperatively to resolve this issue," he said.
Al Jazeera's Yusuf Sharif in Ankara says Turkey is unlikely to send troops into its neighbour in the near future given that it is due to host a regional conference next month with Iraqi representatives among the attendees.
Sharif also said that the government in Baghdad wants time for a recent security agreement signed with Turkey to take effect.
Yusuf Kanli from the Turkish Daily News
said while there was public pressure on the Erdogan government to show it was able to deal effectively with PKK rebels it needed to differentiate between the group and the wider Kurdish issue.
"You can not end this kind of terrorism through military action, there are other factors to consider such as political, and social elements that intermingle," he told Al Jazeera.
"But Turkey can not in any way ignore the need to provide security for its country. They have to differentiate between PKK and the Kurdish problem."