The boat capsized Thursday of Indonesia's south Java coast, leaving as many as 50 people, including 30 children, dead or missing, the Australian Broadcasting Corp. reported.
"I called the Australian government like 12 times. I told them we have 35 children," one survivor said, adding that he told authorities that, "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."
The survivor, whose name was not reported, said the first call to Australian authorities was made Thursday, when the asylum seekers' boat engines broke and the boat began taking on water. Help didn't come for more than 24 hours, the survivor said.
Australian Immigration Minister Scott Morrison issued two statements denying that it took more than 24 hours for help to come to the asylum seekers.
Morrison said Australia didn't receive a call for help until Friday, at which point authorities coordinated a search and rescue operation.
Survivors of the boat sinking also alleged that members of the Indonesia military were the ones who brought the asylum seekers to the boat to be smuggled into Australia.
"The army took us," another survivor said. "The army was driving the cars."