The ground and air offensive, which began Saturday, is pushing into the tribal region from three directions, led by about 28,000 troops with air and artillery support, The New York Times reported.
Military spokesman Maj. Gen. Athar Abbas told reporters that after three days of fighting, security forces were in command of areas overlooking Kotkai, the hometown of Taliban suicide bomb instructor Qari Hussain, the report said. Government troops also had secured the northern Sherwangi area.
The spokesman said 18 militants were killed in the past 24 hours and that security forces had lost two of soldiers while another 12 soldiers were wounded. Since Saturday, 78 militants have died, officials say.
The casualty claims cannot be independently confirmed as no journalists are accompanying the troops.
Abbas said there are about 5,000 to 10,000 Taliban militants in the region, assisted by another 1,000 foreign militants, who were offering tough resistance.
Pakistani officials say South Waziristan tribal region is where the militants plotted their recent series of deadly attacks, The Washington Post said.
The Post report quoted military officials as saying nine soldiers have died since Saturday.
Notable deaths of 2014 [PHOTOS]