The CNN footage showed buyers bidding for the migrants, who were sold off for as little as US$400 ($587) each.
One west African man told the television network: "Sure, I was sold".
Others recounted how they were beaten by their "owners" as they put to work.
Ahmed Metig, the deputy prime minister of the UN-backed Government of National Accord in Tripoli, said the allegations would be investigated.
He said he would establish a "commission to investigate these reports in order to apprehend and bring those responsible to justice".
Alpha Conde, the president of Guinea and chairman of the African Union, where many migrants come from, called for an inquiry and prosecutions relating to what he termed a "despicable trade... from another era".
The Senegalese Government called the apparent slave market a "blight on the conscience of humanity".
Migrants who are rescued at sea and brought to Italy have told how they are beaten, tortured and in some cases raped by traffickers in Libya.
Many young women end up as prostitutes on the streets of Italy, with Nigerian girls as young as 13 forced to sell themselves for as little as €10 ($17) a time, terrified into submission by gang rape and voodoo curses.
It is estimated that 80 per cent of Nigerian teenage girls and young women who make it to Italy are forced into the sex trade.