Turkish troops pursued Kurdish rebels in northern Iraq on the third day of a major ground operation on Saturday as the military put the initial death toll from the clashes at around 50.
Iraq has protested against the operation launched on Thursday evening and the United Nations and Western powers have called for restraint.
At least 24 members of the separatist Kurdistan Workers' Party (PKK) and five soldiers were killed in the clashes, the military said overnight.
It estimated that at least 20 other rebels were killed by artillery and helicopter fire, but said the exact toll would not be known until troops reach the targeted area.
The military also reported panic among the PKK, which is believed to have been caught by surprise.
Turkish incursions into northern Iraq, which were frequent in the 1980s and 1990s, were usually launched with the spring thaw in the rugged, snow-bound mountains of the region when PKK militants begin to sneak into Turkey.
"It has been understood from preliminary information that the terrorists have suffered heavy losses," the military said. "According to intelligence, the (PKK) leaders are trying to flee the region, running southwards in panic."
Heavy fighting and artillery fire continued late into the night Friday, villagers in the area told AFP.
They reported hearing sustained exchanges of automatic fire in the Hakurk and Sidekan regions, on the Iraqi side of the border across from the Turkish town of Cukurca, as fighter planes and helicopters flew reconnaissance missions throughout the night.
Sustained artillery fire could be heard until midnight (2200 GMT) in the Bamerni area, about 40 kilometres to the southwest, where the Turkish army has maintained a small base since the 1990s, the villagers said.
The soldiers poured into the Kurdish region of northern Iraq from 7 pm (1700 GMT) Thursday after eight hours of air and artillery strikes.
Ankara says an estimated 4,000 PKK rebels are holed up in northern Iraq and use the region as a springboard for attacks on Turkish territory as part of their bloody campaign for self-rule in Kurdish-majority southeast Turkey.
Their separatist campaign has claimed more than 37,000 lives since 1984.
Turkish newspapers on Saturday hailed the incursion.
"Winter crackdown on terrorist den," the liberal Milliyet headlined on its front page, while the popular Vatan called for "Vengeance for the martyrs".
But several columnists warned against staying too long in the region and urged the government to back up military measures with economic, social and democratic reforms to win over Turkey's sizeable Kurdish community.
Iraqi leaders on Friday summoned Turkey's charge d'affaires in Baghdad to protest against the operation and Ankara quickly gave assurances on the nature and scope of the incursion.
"The target, purpose, size and parameters of this operation are limited," Prime Minister Recep Tayyip Erdogan said. "Our armed forces will come back in the shortest time possible as soon as they achieve their objectives."
It was the second land incursion the military reported since October, when the government won parliamentary approval for cross-border military action against the PKK.
Turkish troops briefly crossed into Iraq on December 18 to stop a PKK unit from infiltrating Turkey; five air raids on PKK targets in the region were also conducted since mid-December with real-time US intelligence assistance.
Iraqi Foreign Minister Hoshyar Zebari estimated Friday that "hundreds, rather than thousands" of troops were involved in the current operation, during which he said Turkish soldiers had destroyed five bridges near the border.
In New York, UN Secretary General Ban Ki-moon said he was "concerned" by the escalating tension and called for restraint.
A similar warning came from the United States, which said it had been notified of the incursion beforehand.
"We were notified and we urged the Turkish government to limit their operations to precise targeting of the PKK, to limit the scope and duration of their operations," White House spokesman Scott Stanzel said.