The Taliban denied the accusations.
Officials said a 10-year-old was beheaded after being seen collecting food from a garbage can at a police checkpoint and the other victim was a 16-year-old, but no further details were given, CNN reported.
The province's governor condemned beheadings, saying they are inhumane and un-Islamic.
Taliban spokesman Qari Yousef Ahmadi told the BBC the militant group was not responsible for the beheadings of any children in the area.
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