There was no independent confirmation of the death toll because journalists and aid workers do not have free access to the district of Kurram.
The military announced the operation on Monday, under pressure from Washington to do more to destroy militant sanctuaries since US Navy SEALs killed Osama bin Laden north of the capital Islamabad on May 2.
"We have cleared the Jawaki, Mantao and Sarkat areas of central Kurram during four days of operations in the region," a security official told AFP on condition of anonymity.
"We have killed 42 militants and injured over 100. Eight soldiers have also been killed. Taliban are on the run and we are marching ahead," he said.
Another official said that at least 40 militants had been killed in Kurram, a flashpoint for sectarian violence between Shiite and Sunni Muslims.
"At least 40 militants have been killed by the forces. Resistance by the militants against the military is very limited," said Shahab Ali Shah, a local government official.
He said that more than 500 families who fled the fighting had registered with the government for shelter. Around 28,000 people are understood to have fled the offensive, but most have sought accommodation with relatives.
Pakistan`s seven tribal districts bordering Afghanistan are rife with a homegrown insurgency. Washington has called the region the most dangerous place on Earth and the global headquarters of Al-Qaeda. (M014/K004)
Editor: Kunto Wibisono
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