The two-minute video clip, which has recently been circulated on social media, allegedly shows Mahmoud al-Werfalli, a senior leader of Haftar's self-styled Libyan National Army [LNA], ordering the execution around 20 detainees.
The video shows the captives wearing in orange jumpsuits, in similar fashion to IS' execution videos, lined up on their knees and shot in the back of the head at point-blank range.
The New Arab could not independently verify the authenticity of the video.
The incident is reported to have taken place last week in the eastern city of Benghazi, where Haftar's forces were battling final pockets of extremists.
Haftar declared war on extremists in Benghazi three years after the 2011 uprising that toppled and killed Libyan dictator Muammar Gaddafi.
Code-named Operation Dignity, the offensive targeted several militant groups which had overrun Benghazi after the uprising.
The National Commission for Human Rights in Libya on Tuesday expressed deep concern over the video, calling for an impartial investigation into reports of war crimes committed by the LNA.
In July, the United Nations called for the LNA, which controls the eastern part of Libya, to investigate reports that it has tortured detainees and summarily executed "at least 10 captured men".
In March, another video allegedly showing Werfalli executing prisoners circulated on social media.
The footage showed the commander shooting dead three men who were kneeling facing a wall with their hands tied behind their back.
In June, two further videos appeared to show summary executions carried out by LNA fighters on his orders.
A video also emerged of LNA troops celebrating by exhuming the dead bodies of Islamist fighters, including their senior leader, Jalal al-Makhzoum, before parading them through town.
Human Rights Watch said in March that the LNA may have committed war crimes, including killing and beating civilians, and summarily executing and desecrating bodies of opposition fighters in Benghazi.
Haftar, who is backed by Egypt and the United Arab Emirates, does not recognise the authority of the UN-backed Government of National Accord based in the capital Tripoli, instead backing an alternate government set up in the country's east.
Reports of the executions come as Haftar is set to meet Libya's UN-backed Prime Minister Fayez al-Sarraj in Paris on Tuesday to discuss a deal to end the political crisis.
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