Two sailors who survived being stranded on a desert island for a week have been rescued after a plane spotted an SOS message written in the sand.

Linus and Sabina Jack, believed to be a couple in their 50s, had disappeared after setting sail from the Pacific island of Weno, in Micronesia, on 17 August.

They were due to reach Tamatam, around 160 miles away, the following day but they never arrived and a search operation was mounted for the 18ft boat.

In pictures: Couple rescued from desert island Show all 5 1 /5 In pictures: Couple rescued from desert island In pictures: Couple rescued from desert island Linus and Sabina Jack were found on Fayu Atoll, Federated States of Micronesia, on 25 August US Embassy Kolonia In pictures: Couple rescued from desert island Linus and Sabina Jack were found on Fayu Atoll, Federated States of Micronesia, on 25 August US Embassy Kolonia In pictures: Couple rescued from desert island Linus and Sabina Jack were found on Fayu Atoll, Federated States of Micronesia, on 25 August US Embassy Kolonia In pictures: Couple rescued from desert island Linus and Sabina Jack were found on Fayu Atoll, Federated States of Micronesia, on 25 August US Embassy Kolonia In pictures: Couple rescued from desert island Linus and Sabina Jack were found on Fayu Atoll, Federated States of Micronesia, on 25 August US Embassy Kolonia

Micronesia’s National Police Maritime Wing, the US Coast Guard, local rescuers and volunteers mounted wide-ranging searches but found no trace of the missing couple or their vessel.

Hope for a successful outcome dwindled until Wednesday, when a search ship 150 miles to the north-east of the Jacks’ intended destination spotted a flashing light.

The US Embassy in Kolonia said someone attempted to signal a coast guard vessel off the uninhabited Fayu Atoll with a torch, which the missing sailors were known to have in their boat.

A search plane was sent over the island to check for signs of life the following morning, photographing the missing couple and their boat on a sandy beach.

They had drawn the letters “SOS” around 20ft high in the sand and could be seen waving to the aircraft from the palm-fringed shore.

Images showed they had built a makeshift shelter from driftwood and leaves on East Fayu island.

The stranded couple used driftwood and leaves to construct a shelter (US Embassy Kolonia)

Just a few metres above sea level, it is comprised of a shallow lagoon surrounded by a coral reef, while the presence of fresh water is the subject of Micronesian legend.

A ship was sent to rescue Mr and Mrs Jack but could not enter the shallow lagoon to reach them, forcing authorities to send two more boats that arrived on Friday.

A spokesperson for the US Embassy in Kolonia said the rescue operation has been “successfully completed” adding: “They are found and are waiting for a ship to take them home.”

Fayu is among more than 600 islands housing a combined total of 103,000 people in the Federated States of Micronesia, which is a US-associated state in the Western Pacific.