A Turkish helicopter went down in Iraq and eight soldiers were killed during a cross-border ground operation that has drawn criticism from the Iraqi government, Turkey's military said Sunday.

Kurdish rebels said they shot down a Turkish military helicopter near the Turkish-Iraqi border.

Turkey's military said the helicopter went down "close to our border" and technicians were inspecting the wreck to determine the cause of the crash. It was not clear if the reported troop casualties were on board the helicopter. Their deaths bring the Turkish toll since the start of the incursion Thursday to 15, according to statements on the military's Web site.

Thirty-three rebels were killed in Sunday's fighting, bringing the rebel death toll since Thursday to 112, according to the armed forces.

The military said clashes with the rebels were taking place in four areas of northern Iraq, but did not specify any location.

"Terrorist hideouts have been effectively destroyed by warplanes, helicopter gunships and artillery," the military said.

It said advancing troops were destroying rebel shelters, logistic centers and ammunition. Retreating rebels were trying to gain time by setting up booby traps under the corpses of dead comrades or planting mines on escape routes, according to the military.

The bodies of five of the 33 rebels killed Sunday had booby traps under them, the statement said.

The rebels of the Kurdistan Workers' Party, or PKK, said they have killed 15 Turkish troops. Turkish news reports said the slain Turkish soldiers included an army major.

Earlier Sunday, Turkish F-16 jets flew into northern Iraq. Armored personnel carriers transported troops, and four long-range guns were positioned at the edge of a helicopter base in the hilltop border town of Cukurca. At least four helicopter gunships were stationed at the base, one of the main support centers for the Turkish operation.

The Turkish military said it attacked rebel hide-outs on Saturday with fighter jets, helicopter gunships and artillery. The hide-outs had ammunition and explosives inside, a military statement said.

Turkey's military released photographs Sunday of its troops in positions behind hilltop snow embankments and walking up snow-covered hills with white ponchos worn over combat gear.

The incursion is the first confirmed Turkish military ground operation in Iraq since the U.S.-led invasion that toppled Saddam Hussein in 2003.

The rebels are fighting for autonomy in predominantly Kurdish southeastern Turkey and have carried out attacks on Turkish targets from bases in the semiautonomous Kurdish region of northern Iraq. The conflict started in 1984 and has claimed as many as 40,000 lives.

Turkey has assured the U.S.-backed Iraqi government that the operation would be limited to attacks on rebels. The United States and European Union consider the PKK a terrorist group.

U.S. Defense Secretary Robert Gates said Sunday while visiting Australia that it will take a broader approach to erode support for the PKK in northern Iraq.

"After a certain point people become inured to military attacks," he said, "and if you don't blend them with these kinds of nonmilitary initiatives, then at a certain point the military efforts become less and less effective."

Iraq's government also criticized the offensive on Saturday, saying military force would not solve the Kurdish problem.

"We know the threats that Turkey is facing, but military operations will not solve the PKK problem," Iraqi government spokesman Ali al-Dabbagh said.

Massoud Barzani, head of the regional Kurdish administration in northern Iraq, warned Turkey it will face large-scale resistance if it targets civilians in its ground incursion.

The Iraqi government said Saturday that fewer than 1,000 Turkish troops had crossed the frontier. Turkish media reports have put the number in the thousands.

On Sunday, the office of Iraqi Shiite cleric Muqtada al-Sadr demanded an immediate withdrawal of Turkish forces from northern Iraq and advised negotiations instead.

"We demand that the Turkish government withdraw its forces immediately from the Iraqi territory and rely on negotiations to solve this conflict," al-Sadr's influential political committee said in a statement. "We call upon the Muslim neighbor Turkey through its Prime Minister Recep Tayyip Erdogan and its Muslim people to be an element of peace and security in the region."