|There have been conflicting reports over the number of Turkish casualties [AFP]|
Separatist Kurdish fighters claim they have shot down a Turkish helicopter as the number of casualties rises from Ankara's military incursion in northern Iraq, amid growing international criticism.
Robert Gates, the US defence secretary, said on Sunday that military action would not solve the Turkish government's problem with fighters from the Kurdistan Workers Party (PKK).
Speaking in Australia, Gates urged Turkey to respect Iraqi sovereignty and improve communication with Baghdad about both the ongoing operation and other efforts against the PKK.
"I think it's important for everybody to bear in mind the importance of the sovereignty of Iraq," he said.
"There has been contact at high levels about this activity that is in northern Iraq right now. I think that there can always be improvement in the timeliness and in the depth of the dialogue ... It needs to be an ongoing dialogue."
Al Jazeera's Laurence Lee in Istanbul said Robert Gate's comments will have some resonance in Turkey, but that there is still widespread political backing for the military operation.
Turkish troops launched a major offensive on Thursday against PKK separatists, who have been fighting for decades to create a Kurdish homeland in southeast Turkey.
Ankara said it was forced to launch the cross-border attack after Iraqi authorities failed to stop an estimated 3,000 PKK members from using northern Iraq as a base to stage deadly attacks against soldiers and civilians inside Turkey.
A PKK spokesman said the group had shot down a Turkish helicopter during clashes in northern Iraq on Saturday.
"At 6pm (15:00GMT) yesterday, our fighters shot down a Cobra helicopter," Ahmed Danees, head of foreign relations for the PKK, said.
He gave no details of casualties but said more information would be released later.
Danees said on Saturday PKK fighters had killed 22 Turkish soldiers since Turkey began the cross-border offensive.
Turkey's military General Staff said in a statement on its website that only seven Turkish troops had been killed.
Verifying information about casualties is difficult as the fighting is taking place in an inaccessible mountain region.
Australia joined those opposing the Turkish offensive on Sunday with Stephen Smith, the foreign minister, calling on Turkey to withdraw its troops from Iraq "as soon as possible".
There have been conflicting reports about the scale of the cross-border operation, the largest in a decade.
The General Staff has not said how many troops are involved, but it said on Saturday fighting was raging in four different areas of northern Iraq, suggesting a large-scale operation.
A senior Turkish military source said two brigades made up of around 8,000 troops were taking part, while Turkish media have put the number of troops at 10,000.
But a senior officer with US-led forces in Baghdad said the number was under 1,000.
The Turkish offensive has concerned the US and EU, which fear a prolonged military campaign inside Iraq would raise the risk of serious clashes between Turkish and Iraqi Kurdish forces and could undermine the fragile US-backed government in Baghdad.
Ali al-Dabbagh, the Iraqi government's spokesman, acknowledged that Turkey was "suffering from the terrorist PKK organisation" but that military action was not the answer.
"We know the threats that Turkey is facing but military operations will not solve the PKK problem," he said.
He said Turkish commanders had assured Iraq that the "operation will be a limited one and it will not violate certain standards that they have set".
A spokesman for Nuri al-Maliki, the Iraqi prime minister, said on Thursday that he had telephoned Reccip Tayyib Erdogan, his Turkish counterpart, urging him to respect Iraq's sovereignty.
Ali Babacan, the Turkish foreign minister, said on Saturday that the PKK was the sole target of the northern Iraq offensive.
The Turkish General Staff said: "The operation will end once our targets have been reached."
Source: Al Jazeera and agencies