Sikakap district police chief Surya Negara said the boat holding 53 people, including three children and four women, was found drifting near small Mentawai island off Sumatra on September 1 after it ran out of fuel.
"They refused to get off the boat, saying that they want to continue their journey to Christmas Island (Australia). They want 2,000 litres of fuel to sail back to sea," Negara told AFP.
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In a letter to a local immigration office, the asylum seekers threatened to go on hunger strike, saying "we will not eat until we die", according to the message seen by an AFP correspondent.
Negara said local authorities have been in touch with the International Organization for Migration (IOM), but as the island was so remote, it takes time to reach the location.
"Up until now, they refused food or medical treatment. But based on our observation they still have enough food on their boat," he said.
Australia is facing a steady influx of asylum-seekers arriving by boat, many of whom run into trouble on rickety vessels in Indonesian waters after fleeing their home countries.
Indonesia has long been a transit country for illegal migration to Australia. Hundreds of boatpeople have died en route to the country this year.
