The Indonesia Search and Rescue Agency evacuated 26 migrants after the local navy found the lifeboat stranded yesterday near Agropeni beach in Kebumen district of Central Java.
The migrants from Pakistan, Bangladesh, Nepal and Iran are being held at the local immigration office in the nearby district of Cilacap, said Imam Prawira, the office's head of investigation and enforcement, said.
Prawira said, according a Pakistani migrant, they rejected around the border by Australia, which transferred them into the lifeboat.
According to Kebumen police, the migrants left for the Australian territory of Christmas Island from West Java last Wednesday. Three days later they arrived around the border but were intercepted by an Australian warship which exploded their wooden boat.
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Australia bought unsinkable lifeboats as part of its policy to deter such boat journeys, but it has refused to confirm the boats' use in sending asylum seekers back to Indonesia.
Indonesia's vast chain of islands is a popular transit point for people fleeing war-torn countries to reach Australia.
But Australia's new government has instituted new policies and refuses to resettle even genuine refugees who arrive by boat, instead sending them to Papua New Guinea or Nauru in the South Pacific.