Turkey said its ground forces had crossed the border to tackle rebels late on Thursday after an air and artillery bombardment.
PM Recep Tayyip Erdogan has said the offensive is limited in scale and troops will return as soon as possible.
The UN secretary general and the US have urged Turkey to show restraint in the offensive.
A Turkish army statement said: "It has been understood from preliminary information that the terrorists have suffered heavy losses under long-range weapons fire and air strikes."
A Kurdistan Workers' Party (PKK) spokesman, Ahmad Danas, earlier said two Turkish troops were killed and eight wounded in fighting.
Neither report can be independently confirmed.Mr Erdogan had told Turks on television: "The target, purpose, size and parameters of this operation are limited.
"Our armed forces will come back in the shortest time possible as soon as they achieve their objectives," he said, insisting that members of the PKK were the sole targets.
Correspondents say the aim is to isolate the organisation and prevent it using northern Iraq as a launch pad for attacks on Turkish soil.
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.Reports from Turkey on the size of the assault force have varied from 3,000 to 10,000 soldiers.
But senior Iraqi Kurdish sources told the BBC the Turkish side had exaggerated the operation, which they believe to be "very, very limited", and in a remote border area.
Turkey's military said the cross-border ground operation backed by the Air Force was launched at 1900 [1700 GMT on Thursday].
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.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.
Top Iraqi Kurdish and government officials are saying there has been no crossing at the Habur bridge, the only major land route into Iraq, the BBC's Jim Muir reports from Baghdad.
Kurdistan Democratic Party militants who control the area in question inside northern Iraq say they have not detected any Turkish forces near any of their own lines.The office of Turkish President Abdullah Gul says the leader phoned his Iraqi counterpart, Jalal Talabani, about the operation on Thursday evening.
Mr Talabani's office confirmed a conversation had taken place during which Mr Gul invited him to visit Ankara officially, and also assured him that any Turkish operations were against the PKK, not against the Iraqi Kurds.
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.