The men, given a clean bill of health on arrival in the Marshall Islands, were dropped off in the capital Majuro by a fishing trawler which found their small wooden boat several hundred kilometres south of the city.
Tatika Ukenio, Boiti Tetinauiko, Bonibai Akau and Moamoa Kamwea told officials they left their home in Kiribati, an island nation more than 650 kilometres from the Marshalls, on March 23.
Although details of their ordeal are still sketchy, they were blown off course by a storm and later turned off their single outboard engine to conserve fuel and began drifting.
When the castaways saw the trawler, they had enough fuel left to get close to the vessel and attract the crew's attention.
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Koo's Fishing Company representative Orlando Paul said the men were "fit and well" after being picked up, so the trawler continued its fishing expedition before returning to Majuro yesterday.
The men were taken to Majuro Hospital, where doctors said they were healthy. They are staying at the Marshall Islands Resort while the foreign ministry and the International Organisation for Migration arrange their repatriation to Kiribati, expected on Sunday.
In January 2014, Salvadoran fisherman Jose Alvarenga washed up in the Marshalls, more than 13 months after he set off from Mexico's west coast with a companion, who died during the voyage.