A local security official says the incident took place in the vicinity of Sharana city, the provincial capital of Paktika.
The official speaking on the condition of anonymity further added that the clash between the police forces broke out after an altercation between the commanders of the two sides.
He said at least three policemen were killed and around 20 others were wounded durin the clash.
The main motive behind the clash has not been ascertained so far and an investigation is underway in this regard, the official added.
The latest infighting among the police forces takes place as the security forces are busy conducting counter-terrorism operations in Paktika and other parts of the country in the Southeast.
Paktika is among the relatively restive province in southeastern parts of the country where the Taliban insurgents and militants belonging to the other groups including the notorious Haqqani terrorist network are actively operating in some of its remote and restive districts.