Members of the Indonesian military have been implicated in a fatal people-smuggling operation that may have killed up to 30 children.

The asylum seeker boat got into trouble last week and broke into pieces just off the south Java coast.

As many as 50 people are either dead or still missing, most of them children.

Another 10 bodies have been recovered, lifting the death toll to 31, with search and rescue operations suspended until this morning.

Those who did survive are helping Indonesian and Australian investigators to identify the people responsible.

The names of two key smugglers have emerged: Abu Saleh and another man called Abu Ali.

And embarrassingly, local authorities have again been implicated as playing a key role in getting the passengers to the boat.

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."

Passengers recall doomed voyage

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.

Locals help asylum seekers who survived the deadly boat accident off the coast of western Java. ( AFP )

The boat then hit rough seas and capsized only 50 metres from the shore.

Survivors said they rang Australian authorities for help on Thursday when both the boat's engines broke.

"I called the Australian Government like 12 times. I told them we have 35 children," one survivor said.

"We don't want to go to Australia, just take us out of the water.

"We don't want to die. It's our mistake, not the children's mistake."

He said help was promised but in 24 hours nobody came.

"The boat just flipped and we start to swim, and [those] who can swim survived," he said.

Morrison rejects claims response took more than 24 hours

Immigration Minister Scott Morrison has issued two statements rejecting survivors' claims that Australian authorities took more than 24 hours to respond.

A section of the boat's hull washed up on the south coast of west Java. ( ABC News: George Roberts )

He said authorities received the first call on Friday and coordinated the initial search and rescue operation.

Labor frontbencher Tony Burke said rather than issuing statements, Mr Morrison should front the media.

"It's not just a challenge to the confidence of the public," he said.

"It's also a direct affront to those people and those officials who are out there working on behalf of the Australian people, and who for the first time in decades have discovered there are no frontbenchers willing to come out and publicly defend them."