The ground incursion into Iraq -- only the second in more than two years -- came after Turkish Prime Minister Recep Tayyip Erdogan vowed to fight the Kurdistan Workers Party (PKK) "to the end" in response to what he called the "cowardly" assault by its fighters.

PKK spokesman Ahmed Denis hit back with a threat to take the rebels' campaign of violence to cities across Turkey if the army did not halt its policy of confrontation.

By morning, the troops had advanced 10 kilometres (six miles) into Iraqi territory in the Qandil mountains where the rebels maintain a network of rear bases in their 26-year-old armed campaign for self-rule in southeastern Turkey, the Iraqi Kurdish security official said.

Turkish troops were operating in the mountains north of the town of Sidikan in Arbil province, one of three that make up the Kurdish autonomous region of northern Iraq, the official said.

Turkish fire killed a 15-year-old girl and wounded her mother and two-year-old brother in Khwakurq village, Sidikan district commissioner Ahmed Qader told AFP.

As Turkish forces crossed the border and advanced into Iraqi territory during the night they killed another three people, a security official said, without specifying whether the dead were civilians or PKK fighters.

Inside Turkey, the rebels kept up their attacks during the night, killing one soldier and wounding another, bringing the military's losses over the past two days to 12, Turkey's Anatolia news agency reported.

Clashes broke out between troops and PKK fighters after the rebels attacked a barracks near the eastern town of Palu, Anatolia said.

The new casualties came as the Turkish premier joined other dignitaries in the eastern city of Van to attend a ceremony to honour the 11 soldiers who died on Saturday -- the bloodiest single day for the army since 2008.

The death toll prompted indignation among ordinary Turks, with many cultural and sporting events cancelled in mourning.

Erdogan had announced a new policy of opening up to Turkey's large Kurdish minority to great fanfare late last year.

But it has faltered amid an opposition outcry that Ankara is bowing to the PKK, as well as persistent rebel attacks and a judicial onslaught on Kurdish activists.

On Friday, the Turkish premier accused rebels of seeking to undermine his government's initiative to boost Kurdish freedoms and investment in the country's impoverished southeast in a bid to peacefully end the conflict.

But on Saturday, the PKK countered that the so-called Kurdish opening was a hoax and that Ankara was still intent on solving its minority problems militarily.

"She is not sincere in dealing with the Kurdish issue and doesn't want to deal with this issue peacefully," spokesman Denis told AFP in the Iraqi Kurdistan regional capital of Arbil.

"Turkey wants to us take us towards war... We will take our operations to all Turkish cities if the government continues its attacks against us," he warned.

Sunday's Turkish ground incursion was only the second since 2008 but it went far deeper than the previous incursion on Wednesday when troops advanced just a few kilometres (a couple of miles) into Iraq before withdrawing.

The conflict with the PKK, considered a terrorist organisation by much of the international community as well as by Ankara, has claimed more than 45,000 lives since it broke out in 1984, according to the Turkish army.

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