Seniloli Tabuatausole was a former soldier with the Republic of Fiji Military Force, who later joined the United Nations Security serving in Libya.
Gen Haftar agreed to the truce "so that Libyan citizens can celebrate this Eid in peace", his spokesman Ahmad al-Mesmari explained.
He also said the secretary-general urged "all parties to respect the humanitarian truce during Eid al Adha and return to the negotiating table to pursue the peaceful future the people of Libya deserve". "The explosion left two people killed and 10 more injured, including a child", the source said.
The site of the attack is close to offices of the United Nations support mission in Libya.
The UN envoy for Libya, Ghassan Salame, had proposed a multi-day truce for the Eid holiday, which begins Sunday.
"We have noted the coordinates of the rocket fire from zones controlled by Haftar's militias south of the capital" and passed them on to the UN mission in Libya (UNSMIL), Mejii said.
Secretary-General Antonio Guterres condemned the attack "in the strongest terms" and called on the Libyan authorities "to spare no effort in identifying and swiftly bringing to justice the perpetrators of this attack".
No side had claimed responsibility for the blast.
But Benghazi, the cradle of the NATO-backed 2011 uprising that overthrew and killed dictator Moamer Kadhafi, has seen repeated attacks both before and since.
In 2017, loyalists of eastern Libyan military leader Khalifa Haftar took over the city.
The Tripoli-based government on Friday responded positively to the proposal, while LNA spokesman Ahmed al Mosmari told a news conference in the eastern city of Benghazi on Saturday that they would abide by the ceasefire from Saturday to Monday.
A Libyan lawmaker is also feared to have been abducted by an armed group in the eastern city, the United Nations and lawmakers said in July.
The night-time attack in the city of Misrata came days after Tripoli said it conducted strikes on Haftar's main forward air base in Jufra, destroying two Ilyushin 76 planes operated by charter companies registered in Ukraine.
United Nations envoy Ghassan Salame had already called several times for humanitarian truces, without success.
At least two people were killed when a vehicle bomb exploded in Libya's eastern city of Benghazi on Saturday, according to local security sources.
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