Late last month, a double car-bombing in the same city claimed the lives of at least 34 people and injured dozens more. The devices appear to have been activated remotely using a mobile phone, according to a military source.
The United Nations Support Mission in Libya (UNSMIL) was quick to condemn the attack, calling reports of civilian casualties "deeply disturbing".
"This heinous act should not provide a justification for revenge attacks. Prompt, impartial investigations should bring perpetrators to justice", the group said. The country has been since split between rival governments in the east and the west, each backed by an array of militias.
Libya has been wracked by violence and divisions since dictator Muammar Gaddafi was toppled and killed in a 2011 NATO-backed uprising.
The LNA was battling militants, including some linked to Islamic State and al Qaeda, as well as other opponents until late a year ago in the Mediterranean port city.
The summary executions are believed to be carried out by Mahmoud al-Werfalli, a special forces commander for the LNA.
Video showed Mahmoud al-Werfalli - who was already wanted by the International Criminal Court over 33 suspected extra-judicial killings - apparently shooting dead the detainees at the scene of the blasts.
Mr Haftar, a possible contender in national elections that could be held by the end of 2018, seized control in Benghazi in May 2014.
Haftar heads a government based in eastern Libya, while an internationally recognized administration has been set up in the western capital of Tripoli.