The Turkish military said the February 21 night attack was a land operation aided by successful air and artillery strikes that targeted camps of the separatist Kurdistan Workers Party (PKK) across the border.
The statement did not say how many troops crossed into northern Iraq, but reports have spoken of some 10,000.
The Kurdish regional government in the largely autonomous region reported Turkish shelling of northern areas. However, they initially denied there had been a ground incursion.
"There were no clashes along the Turkish-Iraqi border between the peshmerga regional forces and the Turkish troops," Jabbar Yawar, a spokesman for the Kurdish region's peshmerga forces, told RFE/RL's Radio Free Iraq late on February 21.
"However, at 11 a.m. today [February 21] there was artillery shelling at Khwakurk, where the Iraqi, Turkish, and Iranian borders intersect. It happened at Bassian, a deserted village. We would expect clashes to take place there between the PKK guerrillas and Turkish forces in this area because [the guerrillas] are the only ones present in this region."
Iraqi Prime Minister Nuri al-Maliki has called on Turkey to respect Iraq's territorial integrity. In a phone call to his Turkish counterpart, Recep Tayyip Erdogan, on February 21, al-Maliki said Iraq considers the separatist PKK rebels a threat to their shared border but urged dialogue to promote security.
The Turkish General Staff's statement said Turkish armed forces attach "great importance" to Iraq's territorial integrity and stability and will return home in "the shortest time possible after its goals have been achieved."
NATO member Turkey has launched several major land offensives into northern Iraq and maintains at least one base and at least three other smaller contingents of troops in Iraq.
Officials in Ankara accuse the PKK of using northern Iraq to stage attacks against Turkey. They have said Turkey has the right under international law to attack the PKK rebels.
The General Staff has previously estimated that there are some 4,000-5,000 PKK guerrillas in northern Iraq.
Outlawed in Turkey since the 1990s, the PKK is also considered a terrorist organization by the United States and the European Union.
The Kurdish militants are fighting for autonomy in Turkey's predominantly Kurdish southeast. Taking shelter in northern Iraq, they have carried out attacks on targets inside Turkey and killed dozens of troops in recent months.
Iraqi authorities have repeatedly urged Turkey to find a diplomatic solution to deal with the PKK guerrillas.
Some reports have said the operation was launched to prevent the traditional annual infiltration of Kurdish rebels into Turkish territory to start fighting in they spring after the winter snow has melted.
More than 32,000 people have been killed since 1984 when the PKK launched its fight for autonomy for the mainly Kurdish-populated southeast of Turkey.
(compiled from agency reports with contribution from RFE/RL's Radio Free Iraq.)
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