The father of a Syrian boy found washed up on a Turkish beach has spoken of the devastating loss of his loved ones.

Aylan Kurdi, three, was found on a Turkish beach after the small rubber boat he and his family were in capsized in a desperate voyage from Turkey to Greece.

A photo of his body has focused the world's attention on a wave of war-and-deprivation-fuelled migration unmatched since World War Two.

Aylan died along with five-year-old brother Galip and his mother, Rehan, leaving their distraught father, Abdullah, to cope with his sudden, overwhelming loss. He said he now wanted one thing only - to sit by the graves of his wife and children.

"My kids were the most beautiful children in the world, wonderful. They wake me up every morning to play with them. They are all gone now," he said.

A Canadian legislator said the family, fleeing the conflict in Syria, had been turned down in a bid for legal entry to Canada even though it had close relatives there offering financial backing and shelter, but Canada's Department of Citizenship and Immigration later denied that assertion.

"There was no record of an application received for Mr Abdullah Kurdi and his family," the department said in a statement, indicating that a bid for another member of the family, Mohammad Kurdi, had been returned as incomplete.

Tima Kurdi of Vancouver, who is Abdullah's sister, initially told Canadian media that the family had embarked on the perilous boat journey only after its bid was rejected.

She later said, however, that no formal request for refugee status had been made on Abdullah Kurdi's behalf, saying one was filed, and rejected, on another relative's behalf.

Accounts of events changed several times as information flowed in from several parts of the world.

Canadian prime minister Stephen Harper said some early accounts contained inaccurate information.

Describing the tragedy, Abdullah Kurdi said the overloaded boat flipped over moments after the captain, described as a Turkish man, panicked and abandoned the vessel, leaving Abdullah as the de facto commander of a small boat overmatched by high seas.

"I took over and started steering. The waves were so high and the boat flipped. I took my wife and my kids in my arms and I realised they were all dead," he said.

In a police statement later leaked to the Turkish news agency Dogan, Abdullah Kurdi gave a different account, denying that a smuggler was aboard. However, smugglers often instruct migrants that if caught they should deny their presence and it was unclear whether he had been trying to protect a smuggler's identity in his statement to police.

The distraught father, who worked as a barber in Syria, added wistfully: "All I want is to be with my children at the moment."

Abdullah Kurdi said the boat, headed for the Greek island of Kos, was only at sea for four minutes before the captain abandoned the vessel and its 12 passengers.

The route between Bodrum in Turkey and Kos, just a few miles, is one of the shortest from Turkey to the Greek islands, but it remains dangerous. Hundreds of people a day try to cross it despite the well-documented risks.

Tima Kurdi's husband, Rocco Logozzo, told The Canadian Press that Abudllah Kurdi told his sister that both boys were wearing lifejackets when the boat capsized but that the protective gear somehow slipped off when the boat flipped.

He said the family had enough money and room in his home to have provided for their relatives in Syria but had not been able to do because the bid was rejected by a system that was designed to fail.

The family lost all hope when the application was denied in June and made the "bad" choice to try to get to Europe by boat, he said.

Earlier, Tima Kurdi had told the Ottawa Citizen that the application for refugee status had been rejected. She later contradicted this account when she said no formal bid for refugee status had been made.

Her relatives lived in the Syrian town of Kobani, which was devastated by battles between Islamic State militants and Kurdish fighters, said Canadian lawmaker Fin Donnelly.

He had told The Canadian Press that he had submitted the application on the family's behalf.

Canadian immigration authorities rejected the application, in part because of the family's lack of exit visas for their departure from Turkey and their lack of internationally recognised refugee status, the aunt told the Ottawa Citizen.

Canada's immigration minister Chris Alexander suspended his re-election campaign to travel to Ottawa on Thursday to determine the facts of the case, a senior government official said.

Hours later, the department said no request had ever been made for Abdullah Kurdi's family.

The photograph of lifeless Aylan Kurdi, seen around the world, has highlighted the desperation of those risking their lives to try to reach Europe, sparking fresh calls for countries to do more to ease their passage.