Islamabad, Pakistan - More than 280 Pakistani families fear they had relatives who drowned when a migrant boat sank off Greece last week, making it one of Pakistan's worst man-made disasters, the government said Friday.

The rusty trawler packed with travelers capsized in the Ionian Sea on June 14 after setting sail from Libya towards Europe on the world's deadliest migrant route.

The death toll stands at 82, with 104 survivors pulled from the water, but witness accounts suggest many hundreds more went down with the ship, with their remains still missing at sea.

Interior minister Rana Sanaullah told parliament that "so far 281 Pakistani families have contacted us and said that their children may be victims of this accident".

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Twelve Pakistanis were among the survivors and Sanaullah estimated that "about 350 Pakistanis were on board".

"Perhaps there has never been such a large toll in any incident before, even in terrorist incidents," he said.

Pakistan is in the grip of a staggering economic downturn that saps families' purses and spurs illegal migration, mostly by young men who hope to get a financial foothold in Europe and send cash home.

The routes they take vary greatly. Some pay for legal transport to North Africa and take their chances from there, voyaging onwards by sea. Others attempt to go overland through Iran and Turkey.

Dodging border guards and police and moving through different jurisdictions with limited funds means that communication with families is often patchy, making it difficult to determine their exact movements.

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Pakistan's Federal Investigation Agency (FIA) is collecting DNA samples from the families in a bid to link them to the remains recovered from the wreck, with 193 blood and hair samples taken so far.

But the number of missing far outweighs the number of bodies recovered, diminishing hope for grieving families who are overwhelmingly from Pakistan-administered Kashmir and eastern Punjab province.

"We should at least get the dead bodies so that the parents and relatives can get peace of mind," said Zafar Iqbal (55), who reported losing two nephews in the incident.

"The government should at least complete the investigation as soon as possible," he told AFP from Bandli village in Pakistan-administered Kashmir.

Punjab and Pakistan-administered Kashmir host a thriving black market of what locals call "agents" – human smugglers who arrange illegal migration to Europe for a large fee.

An FIA official in Islamabad told AFP on Friday that "so far 25 agents have been arrested".

"Raids are being conducted against the human traffickers and the investigation is ongoing," the official said.