Ankara says it targeted PKK bases but Baghdad claims Kurdish villages were hit.
There were no reports of any casualties from what a Turkish military official described as “a limited clash” with the separatists.
“Two PKK groups were spotted just across the border and it was determined that they were planning attacks and a battalion of soldiers intervened,” the military official told the Reuters news agency.
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Jamal Abdullah, a spokesman for the regional Kurdistan government, told The Associated Press news agency that the soldiers had withdrawn about 15 hours after entering.
“The area they entered is a deserted area and there is no Iraqi force or peshmerga deployed there,” he said.
A website linked to the political party of Jalal Talabani, the Iraqi president who is Kurdish, said as many as 700 Turkish troops had gone as far as 8km into Iraq.
Fouad Hussein, head of the office of Kurdish regional president, Massoud Barzani, said: “We condemn this incursion.
“Turkey wants to transfer the problem on to the territory of Iraqi Kurdistan.”
Turkey says it has a right to use force to combat the estimated 3,000 separatists who shelter across the border northern Iraq.
Abdullah Gul, Turkey’s president, said on Tuesday that Ankara’s only goal was to target the PKK.
“There are no other goals. Iraq is Turkey’s neighbour and we want to save the Iraqis from this trouble of terror,” Gul was quoted as saying by state news agency Anatolian.
Turkish fighter jets bombed villages in northern Iraq over the weekend and the government in Baghdad complained that at least one civilian woman was killed.
The UN refugee agency said on Tuesday that Turkish bombardment had forced 1,800 people to leave their homes.
“The shelling is apparently ongoing and we don’t know if more people are displaced,” Astrid van Genderen Stor, UNHCR spokeswoman in Geneva, said. “Winter has set in and living conditions are very harsh.”
Meanwhile, US military commanders and diplomats in Iraq said they did not know Turkey was sending warplanes to bomb in northern Iraq until the jets had already crossed the border.
Americans have been providing Turkey with intelligence to go after Kurdish separatists in northern Iraq.
A co-ordination centre had been set up in Ankara so Turks, Iraqis and Americans could share information, two US officials said on Tuesday.
The officials, speaking on condition of anonymity, expressed anger that they were told of Sunday’s attack only after it was already under way.
Their comments follow complaints by Iraqi leaders that Turkey had not co-ordinated with Baghdad before sending bombers to strike PKK targets.