The International Federation of the Red Cross and Red Crescent (IFRC), citing the Libyan Red Crescent, said on its website that the African migrants had been trapped for "four days" in the metal container.
Some of the 56 who survived were "suffering from various injuries and fractures and needed immediate medical attention".
The migrants were found early Tuesday in the coastal town of Khoms, east of the Libyan capital Tripoli, Mohamad al-Misrati, a Red Crescent spokesman in Libya, told AFP.
A Khoms resident, on condition of anonymity, told AFP that the container had been on a truck headed for a beach in Khoms, from where the migrants were expected to board a boat for Europe, when it was stopped and searched at a checkpoint.
The Red Crescent branch at Khoms said on its Facebook page that the survivors and the 13 bodies were found "dumped" outside a detention centre for migrants in the town.
Fawzi Abdel Ali, a Red Crescent spokesman in Khoms, told the IFRC that "when volunteers arrived, they provided first aid, psychological first aid, food and blankets for the 56 survivors, among them a five-year-old girl called Aisha".
Most of them were also from sub-Saharan Africa.
People smugglers have taken advantage of the chaos gripping Libya since its 2011 revolution that toppled and killed dictator Moamer Kadhafi to boost their lucrative trade.
Most departures take place from the west of Libya, usually heading for Italy 300 kilometres (190 miles) away across the Mediterranean.
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