Indonesian troops have been implicated in a fatal people-smuggling operation last week.
An asylum seeker boat got into trouble on Thursday and broke into pieces just off the coast of south Java. As many as 50 people are either dead or still missing.
Another 10 bodies have been recovered, raising the death toll to 31.
Those who did survive are helping Indonesian and Australian investigators to identify the people responsible.
The ABC reports the names of two key smugglers have emerged: Abu Saleh and another man called Abu Ali.
Survivors said Indonesian soldiers helped ferry them to the coast where the doomed boat was waiting.
"The army took us," one survivor said. "The army was driving the cars."
The passengers said engine trouble began on Thursday and the boat started taking water, forcing them to turn back to Indonesia.
Eventually, the motor pumping water off the boat ran out of petrol and the boat started taking on water. The ABC reports the boat then hit rough seas and capsized only 50 metres from the shore.
Immigration Minister Scott Morrison has issued two statements rejecting claims by the survivors that Australia took more than 24 hours to respond.
He said the Australian Maritime Safety Authority received the first call on Friday and co-ordinated the initial search and rescue operation.