More than 30 migrants from Bangladesh who were trapped on a merchant ship off Tunisia for three weeks have been sent back to their home country against their will, according to relatives.

They were among 75 migrants rescued on 31 May by the Maridive 601, an Egyptian tugboat that services offshore oil platforms, only to spend the next 20 days at sea near the Tunisian coast.

The migrants disembark in Tunisia. Photograph: Forum Tunisien pour les Droits Economiques et Sociaux

The International Organization for Migration, an intergovernmental organisation linked to the United Nations, said the Bangladeshis “wished to return home”.

But relatives and aid groups claimed that when a Bangladeshi envoy visited the boat the migrants were forced to accept their repatriation under the threat of having food, water and medical treatment being taken away.

One relative told the Guardian: “When all the people were on the boat, they were told by the Bangladeshi embassy that if they didn’t agree to sign, they would not get any food or water any more. The people were afraid to die on the boat. The Bangladeshi embassy forced them to sign.”

On 18 June, the 75 migrants, who included Egyptian, Moroccan and Sudanese people, were taken off the Maridive 601 and transferred to a Tunisian detention centre.

The people gather in the reception centre where they are being held before being sent back.

The IOM confirmed that a few days later the first 17 individuals were returned to Bangladesh, and on 24 June, another 15 migrants were sent back.

It said “more migrants will be travelling in the coming days, according to their decision”.

The Forum Tunisien pour les Droits Economiques et Sociaux (FTDES), an independent organisation that aims to defend economic and social rights, said: “We doubt that the decisions to return were made voluntarily by the migrants.

“We have tried to visit the migrants in the reception centre in order to inquire about their wellbeing but despite making repeated inquiries and requests, the whereabouts of the detained migrants was not revealed.”

Another relative said: “I spoke with my brother this morning in the centre. He is scared to be returned to Bangladesh, like all the people there. Nobody wants to return to Bangladesh; everyone who is returned is forced.”

The IOM’s head of mission in Tunisia, Lorena Lando, rejected the accusations. “None of the migrants has been deported; [they] wished to return,” she said. “IOM does not do deportation, nor force anyone to return.”

Lando said the IOM “did not have access” to the migrants until 19 June, after the Tunisian authorities allowed their disembarkation.

She added: “Remaining at sea was not a solution either. It is up to the person to also apply for asylum if they fear persecution … or seek help to return home or take time to decide.”

A spokesperson for Alarm Phone, a hotline service for migrants in distress at sea that was alerted to the ship’s plight by crew members, said: “The IOM refers to such deportations as voluntary returns but what is voluntary about telling survivors that they can leave their prison merely if they agree to be returned?

“Do we really believe that these Bangladeshi people risked their lives to move to Libya and then to try to cross the Mediterranean, only to then be ‘voluntarily’ returned to Bangladesh?”