The New York-based organization on Wednesday urged the LNA to keep promise to investigate the latest killings.
Police found the corpses of 36 men, all of them executed, near the town of al-Abyar, east of Libya's second city Benghazi, on October 26. Two days later, Haftar ordered an investigation but no findings have been declared and no suspects have been arrested.
"The LNA's pledges to conduct inquiries into repeated unlawful killings in areas under their control in eastern Libya have so far led nowhere," said Eric Goldstein, deputy Middle East and North Africa director at the HRW.
"The LNA will be condoning apparent war crimes if their pledge to investigate the gruesome discovery in al-Abyar proves to be another empty promise," he added.
Back then, a local security official said the bodies discovered in al-Abyar belonged to suspected Takfiri militants, including 19 foreigners.
The HRW said it had “reviewed multiple lists containing a total of 25 names of men found at al-Abyar, but could not verify which were civilians and which, if any, were fighters affiliated with forces opposing the LNA.”
However, the rights group cited the relatives of six of the victims as saying that they were civilians who had been taken by armed men affiliated to LNA from their homes in presence of their family members.
The HRW also urged the LNA to hand over a senior military commander wanted by the International Criminal Court in connection with previous killings.
In August, the ICC issued a warrant for the arrest of Mahmoud Mustafa Busayf al-Werfalli, a commander of the Benghazi-based Al-Saiqa brigade, on suspicion of involvement in war crimes, including the execution of 33 people in Benghazi.
The ICC judges accuse Werfalli of personally shooting or ordering the execution of people who were either civilians or injured fighters in at least seven incidents in 2016 and 2017 that were filmed and posted to social media sites.
The LNA has said Werfalli is already in custody and will be tried by a military tribunal.
Libya has been experiencing a power vacuum since a NATO military intervention resulted in the downfall of its longtime dictator Muammar Gaddafi in 2011. Since then, the country has been grappling with chaos and the emergence of numerous militant groups, including the Takfiri Daesh terror group.
Libya currently has two governments, one based in the capital, Tripoli, and the other based in the eastern city of Tobruk. Libyan military commander General Khalifa Haftar in Tobruk does not recognize the authority of the Tripoli-based the Government of National Accord (GNA), which is recognized by the UN.