Reuters reported that Afghan officials confirmed the incident on Wednesday, a video of which had gone viral on social media.
Most of the 2,600km border has been fenced by the Pakistan military despite the Afghan Taliban's stance against the border.
Afghan defence ministry spokesman Enayatullah Khwarazmi was quoted as saying by Reuters that everything was now normal. He stated that the Taliban soldiers had tried to stop the Pakistan Army from erecting what he termed an 'illegal' border fence along the Afghan province of Nangarhar.
Pakistani authorities have not reacted to the incident and Reuters' request for comment is said to have been denied.
A video that went viral on social media showed Taliban soldiers had taken control of spools of barbed wire and a senior official could be heard warning Pakistani soldiers deployed in security posts against fencing the border again. However, the video could not be independently verified.
Meanwhile, Taliban spokesman Bilal Karimi said they were carrying out an investigation into the matter.
Two Taliban officials told Reuters that the Taliban authorities and Pakistani soldiers faced a standoff over the border incident, adding that the situation was tense.