The Federal Government rejects claims the 14 Turkish Kurds who arrived on Melville Island north of Darwin last week requested refugee status.
The 14 men are now in Indonesia after being towed there over the weekend.
They have told the ABC they informed Australian authorities that they were refugees and they wanted to stay in Australia.
Immigration Minister Amanda Vanstone says as far as she knows, they did not make a claim for refugee status.
But she says that is irrelevant, as Melville Island had been excised from Australia's migration zone.
"They weren't in Australian territorial waters, they don't have an opportunity to demand where they're taken for processing," she said.
Senator Vanstone says the men's claims for asylum will be processed by the United Nations High Commissioner for Refugees.
The UNHCR's Australian representative Michele Gabaudan says Australia has breached the international refugee convention.
"Australia has shirked its responsibility," he said.
The UNHCR is waiting for access to the 14 men.
Indonesian police say the men are now at an immigration office on the island of Ambon.
"We took care of them for several days because when they reached here their condition was unfit for any travel," regional police chief Ahmad Yani said.
Asked why he did not expel the 14 Turkish Kurds as indicated by a senior police general in Jakarta over the weekend, he said: "That would be inhumane and impossible".
"Besides their poor health, their boat condition was also very bad and too small. You actually can't call it a boat."
He told the Reuters news agency he does not know what will happen to the men, but he assumes they will be put into International Organiation for Migration shelters on Java or Lombok islands.
