It comes after several videos were posted online showing its men killing captured fighters.
The Libyan National Army (LNA) took over Benghazi's south-western district of Ghanfouda on Sunday following weeks of fighting.
The graphic videos have been condemned by Libyans and human rights groups.
In one piece of footage, a senior LNA commander kills three men lined up against a wall on their knees; they were shot at point-blank range.
In another, soldiers drag a captured, unarmed man, who they believe is a militant. He gets thrown into a pile of rubble, slapped, and is asked if he has anything to say before he dies.
Then at least three in the group can be seen opening fire on him with assault rifles.
In a statement, the LNA condemned the summary executions and said they were individual acts not sanctioned by top commanders.
The LNA's General Command says it has asked army unit chiefs to hand over the men shown in the videos to military police for questioning. They say the perpetrators will be held to account for their actions.
The alleged violations came after the LNA captured the last block of buildings in Ghanfouda, where fighters and civilians were holed up for weeks.
Libya's second city has been a battleground since 2014 as a patchwork of army units and other armed groups loyal to them has fought against a coalition of Islamist militias.
Human Rights Watch told the BBC it had spoken to relatives of civilians who said several family members had been detained by the LNA.
There have also been unconfirmed reports of civilians being killed as they tried to escape. Some of them are believed to be relatives of fighters.
Hanan Salah, the senior Libya researcher at Human Rights Watch, said: "Fighters aligned with the Libyan National Army in eastern Libya seem to have torn up the rule book, as they stand accused of summary executions, desecration of corpses of opposing fighters and attacking civilians with impunity.
"The army's leadership in the east needs to know that they carry individual responsibility over the forces under their command and can be implicated in what appear to be war crimes, unless they act immediately to stop such violations and hold perpetrators to account."
Libya's eastern-based self-styled army says it is investigating abuses allegedly committed by its fighters in the city of Benghazi.