The powerful army chief told commanders of units deployed along the western border with Afghanistan that they had "full liberty of action to respond (by) employing all capabilities" available at their disposal, the sources said.
Kayani was quoted by the sources as saying that there should be "no ambiguity in the rules of engagement for everyone down the chain of command" if they faced an attack by NATO forces.
Such an action would "require no clearance at any level" and the army would "provide resources as required on ground", he was quoted as saying.
Following Saturday's air strike on two military border posts in Mohmand Agency that killed 24 soldiers, Pakistan closed all NATO supply routes and asked the US to vacate Shamsi airbase, reportedly used by CIA-operated drones.
Pakistan also decided to boycott the Bonn Conference on Afghanistan to protest the attack.
The sources said Kayani had described the NATO attack as a "blatant act of aggression" that was "unacceptable".
The army chief said he had issued directions that "any act of aggression" would be responded to with "full force, regardless of the cost and consequences".