The captain of an Egyptian tug that retrieved 75 migrants appealed Monday to Tunisian authorities to allow his vessel to dock, as NGOs reported food shortages and sickness on board.
"I request that the Tunisian authorities allow us to make an emergency entry to Zarzis port", Faouz Samir, captain of the Maridive 601, told AFP.
"The migrants' state of health is bad - many are suffering from scabies", he added.
The vessel, which services oil platforms between Tunisia and Italy, arrived at Zarzis in southern Tunisia on Friday evening, after picking up the drifting migrants in international waters that morning.
A doctor was able to board the boat, according to the Red Crescent.
"Four people are in a condition which requires medical intervention," said Mongi Slim, a Red Crescent official in southern Tunisia, adding most of the cases were infectious scabies.
Sixty-four of the 75 migrants were Bangladeshi and at least 32 of those on board were minors and unaccompanied children, according to the International Organisation for Migration.
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They "urgently need water, food, clothes, blankets and above all medical assistance," the IOM said, adding it was ready to help Tunisia provide for the migrants.
Photos published online by the Tunisian Forum for Economic and Social Rights, an NGO, showed migrants lying on the deck of the boat, while sailors attempted to feed them.
Contacted by AFP, Tunisia's central government and local authorities did not wish to comment.
"We understand the difficulties and the scale of the challenges that migration flows pose and we are working to support relief and assistance capacities," said Lorena Lando, the IOM's head of mission in Tunisia.
"But we are worried by the increasingly restrictive policies adopted by several countries."
Last month, around 60 migrants, most from Bangladesh, drowned off the coast of Tunisia after leaving Libya on a boat bound for Europe.
There has been a significant reduction in rescue vessels operating in the Mediterranean in recent months, with humanitarian boats facing legal woes as countries such as Italy impose a hardline migration policy.