The military on Wednesday issued a statement in which it said Afghanistan's response to Operation Khyber-4 was "unwarranted".
"The (response) runs counter to Pakistan Army’s efforts for better Pak-Afghan coordination and cooperation," Inter-Services Public Relations said in its statement.
"The information about Operation Khyber-4 has been shared (twice verbally and in written) with Afghan Forces as well as Resolute Support Mission, and ODRP."
The Afghan defence ministry had earlier said Pakistan's military offensive "needs to be launched on both sides of the Durand Line". It also claimed no contact was established with the Afghan forces over the military operation.
Pakistan says 'Khyber-4' will target the Islamic State militant group making inroads into areas bordering Afghanistan.
Military spokesman Lieutenant General Asif Ghafoor said Islamic State was growing in strength inside Afghanistan, prompting the military to launch an operation in Federally Administered Tribal Areas (Fata).
"This operation was necessary because Daesh is getting established there and we have to stop the influence of Daesh spreading into Pakistani territory through the Rajgal valley," Ghafoor said, referring to a valley surrounded by mountains reaching up to 14,000 feet.
He said that the operation, which would include the Pakistan Air Force, would focus on the border areas inside the Khyber Agency area, which is part of Fata.
"Once this operation is completed, we will first secure the international border on our side and eliminate the hideouts of various terrorist groups," Ghafoor added.