The troops noticed suspicious movement along the LoC in Kupwara late on Monday night and challenged the intruders. There was a brief exchange of fire between the two sides, the officials said.
Police officials said the two operations were launched on August 28 based on specific inputs by Kupwara Police a day earlier.
At least two terrorists are believed to be hiding in the area. No casualties have been reported so far.
India on Thursday reacted strongly to reports of Pakistan setting up a special group to "expose" New Delhi's alleged atrocities in Kashmir, saying it should focus its energies on "stemming the rot of terrorism instead of expending its breath" in making baseless charges.
Brigadier, Northern Command, S Gotra said the Indian Army launched a counter offensive along the LoC in retaliation to Tuesday's offensive in Machhil.
This is the second such incident of mutilation of the body of an Indian soldier on the LoC since October 29.