The trio — Samuel Pelesa and Filo Filo, both 15, and Edward Nasau, 14 — had been given up for dead on their coral atoll in the Tokelau islands, where a memorial service was held for them after extensive searches failed to find them.

The boys set off on Oct. 5 in their aluminum dinghy from their home island to one nearby. It’s not known how they went missing, but the outboard motor on their boat may have broken down at sea.

Worried family members reported them missing and the New Zealand air force launched a sea search. No sign of the tiny boat was found.

On Wednesday, the tuna boat San Nikuna spotted a small dinghy bobbing in the open sea northeast of Fiji, with three people aboard waving frantically, said first mate Tai Fredricsen. They had drifted 800 miles from where they set out.

“We saw a small vessel, a little speedboat on our bows, and we knew it was a little weird,” Fredricsen said.

The fishing boat pulled up alongside the smaller vessel and asked the teenagers if they needed any help, to which they readily replied that they did.

“All they could say was ‘thank you very much for stopping,” Fredricsen told New Zealand’s National Radio on Thursday by phone from the ship. “In a physical sense, they look very physically depleted, but mentally — very high.”

The teens and their boat were hauled aboard the fishing trawler, which was on its way to Fiji Friday where it would deliver the trio into medical care.

Fredricsen said the boys were dehydrated, sunburned and very thin, but otherwise seemed well. The tuna boat’s crew gave them small portions of fruit and fluids.

Fredricsen said the boys reported having just two coconuts with them when they set out. During their ordeal, they drank rainwater that collected in the boat and ate fish they had caught. Once, they managed to grab a sea bird that landed on the boat and they devoured that, Fredricsen said.

The rescue came not a moment too soon: Fredricsen said they had begun to drink sea water because it hadn’t rained in the past few nights.

He said the waters where the teenagers were spotted are very isolated and commercial vessels rarely pass through. The San Nikuna was there trying to shorten its return journey to New Zealand.

The boys come from the atoll of Atafu, one of three that comprises the tiny Tokelau island group where 1,500 people live.

The teens were able to telephone home from the San Nikuna, where one of them spoke to his grandmother and gave them the news that they were alive.

“It’s a miracle, it’s a miracle,” said Tanu Filo, the father of Filo Filo. “The whole village, the whole village, they were so excited and cried and they sang songs and were hugging each other. Everybody was yelling and shouting the good news,” he told Radio New Zealand International.

Atafu, Nukunonu and Fakaofo, picture-perfect South Pacific islets, lie 300 miles  north of Samoa, surrounded by 128 mostly uninhabited coconut palm-covered islets. The territory has a total land area of just 4.7 square miles.