The children, aged 15, 12 and 10, were urged by their mother and father to swim to a distant rocky outcrop, as their parents desperately clung to their three-year-old son and the overturned boat off Australia's Cape York Peninsula on July 6.

"It was the last time we saw them," Stephen Nona, 12, told the Sydney Morning Herald on Wednesday. The three children were rescued on Monday.

With no water on the outcrop, the children had to brave the sea to reach another island.

"We have to swim or we'll die," Stephen told his sisters Ellis, 15, and Noritta, 10, as they stood on the barren outcrop.

"We swam all day. We started in the morning and we got to the big island in the afternoon. I found a coconut and skinned (the husk) with my teeth," Stephen was quoted by the newspaper as saying.

The Torres Strait Islander family had set out from their home on Badu Island in the Torres Strait to travel 40 miles to Thursday Island to attend a birthday party -- a routine journey for people who live on scattered islands between Australia's tropical north and Papua New Guinea.

But after 15 miles the dinghy's motor broke down. The children's father Naseli, an experienced seaman, repaired it but the anchor rope became entangled in the motor and the boat capsized.

In the choppy waters, Naseli and his wife Dosena supported their three-year-old son, Clarence, who was wearing a lifejacket, and yelled at their other children to try and swim to the safety of a rocky outcrop about a half-mile away.

As the children swam through the wind-swept sea they kept looking back, seeing their parents and little brother drifting off into the distance, with only one life jacket between them.

Stephen, Ellis and Noritta eventually made it to the island where, wet and frightened, they huddled together and scanned the sea for their parents. "We prayed to God to bring them, but they did not come," said Stephen.

OYSTERS AND COCONUTS

The children stayed on the rocky outcrop for three days without fresh water. They drank small amounts of seawater and ate the few oysters they could break open with stones. Last Friday, Stephen decided they must swim to another island to survive.

"When they got tired, I swam behind, pushing them along," he said. "The tide was slow. The wind blew waves against the tide, into our faces."

After swimming all day they reached Matu Island, an atoll about the size of a football field with one coconut tree. The children had swum a total of about 2 1/2 miles through open sea from where their boat had capsized.

For the next three days and nights the children survived on five coconuts, eating coconut flesh and drinking coconut milk, and a few oysters, until they were rescued.

Torres Strait Islanders are a seafaring people and boat journeys between islands can often take days as weather and sea conditions change. The alarm was not raised for a week when the family had not returned to Badu Island.

On Monday, the children's uncle, knowing the tides and currents, located the castaways within a few hours.

"They were very good swimmers, but we are glad they had Stephen with them because the two sisters would probably have given up or panicked," said their aunt, Wendy Phineasa.

"We teach all our children survival skills on the islands. It's like teaching city kids to cross the road," Phineasa told Reuters by telephone from Badu Island on Wednesday.

The Australian Maritime Safety Authority said on Wednesday it had called off the search for the children's parents, but relatives and friends refused to give up hope and said they would continue searching in eight small boats.

"Some of them are really sad but the majority are feeling there's still hope they're out there somewhere," said Phineasa.

"There are many small islands and the men are landing on them and going by foot, yelling their names, looking for signs of survivors," she said.