Turkish ground forces have rolled across the border into northern Iraq to target Kurdish rebels said to be sheltering there.
Thousands of soldiers are thought to be involved in the operation which, the army says, began on Thursday evening after an air and artillery bombardment.
Turkey promised its force would "return home in the shortest time possible after its goals have been achieved".
The US military says it believes the operation is "of limited duration".
But a US official quoted by Reuters news agency appeared to express concern about the scale of the Turkish operation.
It was "not the greatest news" and marked "a whole new level", Deputy Assistant Secretary of State Matthew Bryza said in Brussels.
While supporting Turkey's right to fight "terrorism", the EU has asked Turkey to "refrain from taking any disproportionate military action".
The Americans are strong allies of Turkey but are also anxious not to see any action which might destabilise Iraq, BBC world affairs correspondent Nick Childs says.
The Kurdish government in the north has been a particularly valuable partner for the US, he adds.
'Unusual timing'
"A cross-border ground operation backed by the Air Force was launched at 1900 [1700 GMT on Thursday]," the military said.
PKK fighters are known to use the northern Iraq as a base
Turkey has carried out at least one, smaller 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.
After Turkish broadcaster NTV reported that 10,000 soldiers had crossed the border on Thursday, a Turkish military source confirmed for Reuters news agency that two brigades had been deployed.
A brigade numbers up to 5,000 troops, the agency notes.
The 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 have 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.
Baghdad 'unaware'
As news of the operation broke, Iraqi Foreign Minister Hoshyar Zebari told the BBC he was not aware of any incursion since speaking to BBC correspondent Jim Muir late on Thursday.
The minister, himself a Kurd from northern Iraq, said he had been in touch with people in the north and in Istanbul, as well as being in close contact with the US.
Rear Adm Smith said the US supported Turkey's "right to defend itself from the terrorist activities of the PKK" and encouraged it to "co-ordinate closely with the government of Iraq".
On Thursday, there was a tense stand-off between Kurdish Peshmerga forces and Turkish troops who had advanced out of the two fixed bases they have inside northern Iraq, our correspondent adds.
The Turkish troops returned to base without shots being fired.
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