The elite force, Tariq Ben Zeyad, led by Saddam Haftar is aimed at "crushing any challenge" to his father's army, which controls "vast swathes of the divided country," Amnesty said as it launched a new report.
Libya tumbled into chaos following the 2011 uprising that toppled dictator Muammar Gadhafi. A multitude of armed groups have been vying for control ever since.
"An unrelenting crisis of impunity in Libya has enabled fighters of the Tariq Ben Zeyad armed group to commit war crimes, and other crimes under international law," the rights group added.
Khalifa Haftar's self-styled Libyan Arab Armed Forces (LAAF) has become one of the most prominent groups in the oil-rich but war-ravaged North African country.
It rules over much of eastern and southern Libya, despite failing to seize the capital Tripoli in a year-long assault in 2019-2020.
Khalifa Haftar, once a candidate in planned post-conflict presidential elections that never took place, backs an eastern-based government challenging that of Abdelhamid Dbeibah in Tripoli.
Since 2016, the force led by Haftar's son Saddam "has terrorized people in areas under LAAF control, inflicting a catalogue of horrors, including unlawful killings, torture... enforced disappearance, rape and other sexual violence," said Amnesty researcher Hussein Baoumi.
The Tariq Ben Zeyad force, named after the eighth-century Muslim commander who conquered the Iberian peninsula, has "no fear of consequences," Baoumi charged.
He called for "a criminal investigation" into Saddam Haftar and his deputy, Omar Imraj.
Their group has forcibly removed "thousands of refugees and migrants" from southern Libya and has been involved in the forced displacement of "thousands of Libyan families" during Haftar's various military campaigns since 2019, Amnesty said.
In November, the International Criminal Court's Karim Khan — the first chief prosecutor to visit Libya in a decade — said he had urged Haftar senior to prevent crimes by his troops.
"Military commanders must prevent, must repress and must punish crimes when they emerge," Khan said at the time.