Sources told Reuters news agency that warplanes had flown up to 20km into Iraqi territory and about 300 ground troops had advanced about 10km.
Thirty-four Kurdistan Workers' party fighters were reportedly killed in attacks on their positions between Sunday and late on Tuesday.
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"I think it is pretty difficult to say troops shouldn't [invade] when the Turkish soldiers are being killed, and their villages attacked"
Celtic, Karlstad, Sweden
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"Further 'hot pursuit' raids into northern Iraq can be expected, though none have taken place so far today [Wednesday]," a military official said.
However, another Turkish official told the Associated Press, on condition of anonymity, that there was no Turkish air strike in northern Iraq, but confirmed that shelling had been carried out by artillery units.
The PKK has been fighting for self-rule in southeastern Turkey since 1984 and Ankara has been angered by the group's use of bases in northern Iraq to stage attacks.
'Eliminate violence'
"We call upon the PKK to eliminate violence and armed struggle as a mode of operation," the office of Massoud Barzani, president of the autonomous Kurdish region of Iraq, said in a statement.
"We do not accept in any way, based on our commitment to the Iraqi constitution, the use of Iraqi territories, including the territories of the Kurdistan region, as a base to threaten the security of neighbouring countries."
On Tuesday, Iraq said it would shut down the operations of the Kurdish separatists in an attempt to head off the threat of an incursion.
"The PKK is a terrorist organisation and we have taken a decision to shut down their offices and not allow them to operate on Iraqi soil," Nuri al-Maliki, the Iraqi prime minister, said.
"We will also work on limiting their terrorist activities which are threatening Iraq and Turkey," he said after crisis talks in Baghdad on Tuesday with Ali Babacan, the Turkish foreign minister.
Iraq also suggested that it would send a high-level delegation to Turkey in a few days to discuss the problem.
But the threat of a full-scale incursion remains despite the extensive diplomacy of the past few days.
'More than words'
As Babacan arrived back in Turkey from Baghdad late on Tuesday, he said: "We need more than words."
"We said that preventing the PKK from using the Iraqi soil, an end to logistical support and all PKK activities inside Iraq and closing of its camps are needed. We also said its leaders need to be arrested and extradited to Turkey."
Turkey's political and military leaders will meet on Wednesday to consider their next move after Babacan said Ankara would not flinch from military action if Iraq and the US failed to clamp down on the PKK.
Ankara is under pressure to act after tens of thousands of protesters gathered on the streets during the funerals of 12 soldiers killed at the weekend.
The mourners chanted slogans condemning the PKK and urging the government to order an incursion.
Eight other soldiers have been missing since the clashes just inside Turkey on Sunday.
On Tuesday, a pro-Kurdish news agency close to the PKK published what it said were pictures of the troops it said were being held by the group. Turkey has not yet confirmed that the soldiers have been captured.