Turkey's military said the land offensive would be supported by fighter jets and Turkish television reported that 10,000 troops had entered Iraq.
"The Turkish Armed Forces, which attach great importance to Iraq's territorial integrity and stability, will return home in the shortest time possible after its goals have been achieved," the General Staff said in a statement posted on its Website.
The military source based in southeast Turkey told Reuters: "Thousands of troops have crossed the border and thousands more are waiting at the border to join them if necessary."
The US military said it was aware that Turkish forces had launched an offensive into northern Iraq against members of the Kurdistan Workers Party (PKK), considered a terrorist group by Ankara, the United States and the European Union.
Rear Admiral Gregory Smith, a US military spokesman in Baghdad, said the operation was understood to be of "limited duration" and specifically targeted at PKK fighters in the largely autonomous Kurdish region in northern Iraq.
"Turkey has given its assurances that it will do everything possible to avoid collateral damage to innocent citizens or Kurdish infrastructure," Smith said in a statement.
Nato member Turkey says it has the right under international law to hit PKK rebels who take shelter in northern Iraq and have mounted attacks inside Turkey that have killed scores of troops. Turkey says it believes some 3,000 PKK rebels are based in Iraq.
NOT THE GREATEST NEWS
A senior US State Department official said the land incursion was "not the greatest news".
"A land operation is a whole new level," Deputy Assistant Secretary of State Matthew Bryza told reporters in Brussels.
He said Washington had been co-operating fully with Turkey in providing intelligence on PKK positions in northern Iraq since last November to enable the Turkish air force to make pinpointed attacks minimising civilian casualties.
The European Union and the United States have in the past raised concern that a major cross-border offensive could destabilise the region, though have not criticised recent small-scale cross-border raids over the past two months.
In Baghdad, Iraqi Foreign Minister Hoshiyar Zebari said his government was not aware of any Turkish ground offensive.
Iraqi Prime Minister Nuri Al Maliki called on his Turkish counterpart on Thursday evening to respect Iraq's borders after renewed shelling. President Jalal Talabani accepted an invitation from Turkish President Abdullah Gul to visit Turkey.
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