On their tenth day at sea, the four Nigerian stowaways crossing the Atlantic in a tiny space above the rudder of a cargo ship ran out of food and drink.

They survived another four days, according to their account, by drinking the sea water crashing just meters below them, before being rescued by Brazilian federal police in the southeastern port of Vitoria.

Their remarkable, death-defying journey across some 5,600 kilometres (3,500 miles) of ocean underlines the risks some migrants are prepared to take for a shot at a better life.

"It was a terrible experience for me," said 38-year-old Thankgod Opemipo Matthew Yeye, one of the four Nigerians, in an interview at a Sao Paulo church shelter.

"On board, it is not easy. I was shaking, so scared. But I'm here."

Their relief at being rescued soon gave way to surprise.

The four men said they had hoped to reach Europe and were shocked to learn they had in fact landed on the other side of the Atlantic, in Brazil.

Two of the men have since been returned to Nigeria upon their request, while Yeye and Roman Ebimene Friday, a 35-year-old from Bayelsa state, have applied for asylum in Brazil.

"I pray the government of Brazil will have pity on me," said Friday, who had already attempted to flee Nigeria by ship once before but was arrested by authorities there.

Both men said economic hardship, political instability and crime had left them with little option but to abandon their native Nigeria. Africa's most populous country has longstanding issues of violence and poverty, and kidnappings are endemic.

Yeye, a pentecostal minister from Lagos state, said his peanut and palm oil farm was destroyed by floods this year, leaving him and his family homeless. He hopes they can now join him in Brazil.

Friday said his journey to Brazil began on June 27, when a fisherman friend rowed him up to the stern of the Liberian-flagged Ken Wave, docked in Lagos, and left him by the rudder. To his surprise, he found three men already there, waiting for the ship to depart. Friday said he was terrified. He had never met his new shipmates and feared they could toss him into the sea at any moment.

Once the ship was moving, Friday said the four men made every effort not to be discovered by the ship's crew, who they also worried might offer them a watery grave.

"Maybe if they catch you they will throw you in the water," he said. "So we taught ourselves never to make a noise."

Spending two weeks within spitting distance of the Atlantic Ocean was perilous.

To prevent themselves from falling into the water, Friday said the men rigged up a net around the rudder and tied themselves to it with a rope. When he looked down, he said he could see "big fish like whales and sharks." Due to the cramped conditions and the noise of the engine, sleep was rare and risky. "I was very happy when we got rescued," he said.

Father Paolo Parise, a priest at the Sao Paulo shelter, said he had come across other cases of stowaways, but never one so dangerous. Their journey paid testament to lengths people will go in search of a new start, he said. "People do unimaginable and deeply dangerous things."