The clash occurred during a clearance operation in Datta Khel area of the tribal district.
A soldier was killed in an encounter with the terrorists, Army said in a statement.
A civilian staff was also killed in the same encounter when he was providing supplies to the fighting force. Six terrorists were killed in the encounter, it said.
It is the second consecutive day of violence in the area after army gunship helicopters destroyed one explosive dump, five vehicles and killed 10 terrorists.
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The Taliban and their ethnic Uzbek allies both claimed responsibility for the attack on Karachi airport, which was seen as a strategic turning point in how Pakistan tackles the insurgency.
Nearly a million people have fled the offensive in North Waziristan, which is aimed at wiping out longstanding militant strongholds in the area, which borders Afghanistan.
North Waziristan has been isolated by deploying troops along its border with neighbouring agencies and Federally Administrative Tribal Areas regions to block any move of terrorists in and out of the Agency.