Monday's clashes took place in the suburb of Hayatabad when a group of five militants attacked a police patrol with small machine guns and Kalashnikovs, police said.
"Three militants were killed during the exchange of fire. We also lost one of our policemen," Shafiullah Khan, a senior police officer, told AFP.
Two militants managed to flee the scene, Khan added.
Khan said that police recovered five grenades, two Kalashnikovs, two small machine guns and explosives from the scene.
Mohammad Ijaz Khan, another senior police official, confirmed the incident and casualties.
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