Iraq's foreign minister has warned that any escalation of Turkey's operation against Kurdish rebels in northern Iraq could destabilise the region.
Iraq says Turkey is damaging infrastructure
Hoshyar Zebari said the "limited" raid into a remote, uninhabited area should end "as soon as possible".
And the Kurdish regional leader said a "massive resistance" would be mounted if civilians were attacked.
Both Turkey and the rebels have given conflicting casualty figures. The US and the UN have urged restraint.
Correspondents say the aim is to isolate rebels of the Kurdistan Workers' Party, PKK, and to prevent them using northern Iraq as a launch-pad for attacks on Turkish soil.
More than 30,000 people have been killed since the PKK began fighting for a Kurdish homeland in south-eastern Turkey in 1984.
The US, the EU and Turkey consider the PKK to be a terrorist organisation.
Turkey said its ground forces had crossed the border to tackle rebels late on Thursday after an air and artillery bombardment.
Ankara says 79 Kurdish rebels and seven Turkish soldiers have been killed in two days of fighting. Rebels said they had killed 22 Turkish soldiers - with "not more than five" PKK soldiers wounded. There is no confirmation.
Reports from Turkey on the size of the assault force have varied from 3,000 to 10,000 soldiers.
Without confirming any figures, PM Recep Tayyip Erdogan, however, has said the offensive is limited in scale and troops will return as soon as possible.
Iraq's foreign minister said his government had only had been informed of the Turkish incursion "in the last minute" - and did not approve it.
"This is a limited military incursion into a remote, isolated and uninhabited region," Mr Zebari told BBC.
"But if it goes on, I think it could destabilise the region, because really one mistake could lead to further escalation."
Mr Zebari said despite a Turkish promise to Baghdad that Turkish troops would "avoid targeting the infrastructure", a number of bridges had already been destroyed.
PKK fighters are known to use northern Iraq as a base
Kurdish region leader Massoud Barzani said the regional government would not be a part of the conflict between the Turkish government and the PKK fighters.
"But at the same time, we stress that if the Turkish military targets any Kurdish civilian citizens or any civilian structures, then we will order a large-scale resistance," a statement from Mr Barzani's office said.
Turkey has carried out at least one ground incursion, as well as frequent air and artillery strikes, against suspected PKK targets in Iraq since parliament authorised the army to act in October 2007.
But this operation's timing is unusual as the mountainous border area is still covered with heavy snow, the BBC's Sarah Rainsford reports from Istanbul.
Nor have there been any major PKK attacks inside Turkey for some time, she adds.
Washington said it had been informed of the incursion in advance and that it had urged the Turks to limit their action to precise targeting of rebel Kurdish targets.
UN Secretary General Ban Ki-moon expressed concern about the situation.
"The protection of civilian life on both sides of the border remains the paramount concern," he said.