The offensive is concentrated in Mohmand district is part of the semi-autonomous region that Washington considers a global nexus of Al-Qaeda and Taliban who plot attacks to destabilise Afghanistan.
"Over the last few days about 22,000 people have been registered in the two camps that UNHCR has helped to set up," UN Refugee Agency spokeswoman Ariane Rummery told AFP.
Amjad Ali, the top administrative official in Ghalanai, the main town of Mohmand, confirmed the number. "We are providing them with food, non-food items and tents," he told AFP.
Ali said the ground and air offensive is targeting local Taliban and other fighters who have fled operations elsewhere in the semi-autonomous tribal belt, including the premier fortress of Waziristan.
An official in Pakistan's Frontier Corps paramilitary said more than 70 militants had been killed over five days of fighting.
The military has claimed victory in a number of battles against militants, perhaps most notably in 2009 in the Taliban's former headquarters of South Waziristan, but militant attacks still continue at large.
Washington has said that eliminating militant sanctuaries in the tribal belt, particularly North Waziristan, is vital in winning the war against the Taliban in Afghanistan and defeating Al-Qaeda.
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