A group of 39 people from Pakistan and Bangladesh were found at Beagle Bay, north of Broome, late last week and have been flown to an offshore detention centre on the Pacific island of Nauru.
Asked if the men would be brought to Australia for treatment, Ms O'Neil said the Nauruan government would be primarily responsible for their care, but didn't rule out medical evacuations.
"It is not our government's intention to use Nauru as the former government did, effectively as a permanent internment camp for people," she told ABC RN.
The Home Affairs minister accused Peter Dutton of 'destructive messaging' about border security. (Mick Tsikas/AAP PHOTOS)
"I'm confident in the conditions that have been provided by the Nauruan government they're doing a good job of it."
Ms O'Neil said discussions with New Zealand about the resettlement of people were ongoing, but couldn't confirm how quickly the men would be processed.
"We're in constant conversation with countries around the world about the management of this problem," she said.
Asked how the asylum seekers were able to reach Australia's shores undetected, Ms O'Neil said the country had a large border.
Opposition Leader Peter Dutton has slammed Labor as "weak and incompetent" on border protection.Â
He said the government needed to explain how many boats had arrived and how they were able to evade detection.
Ms O'Neil said funding for border security was increased by $470 million by her government.
"We should not telegraph to people smugglers or anyone else about the specifics of how we are patrolling our borders," she said.
"The most important thing is that Operation Sovereign Borders is sacrosanct," she said.
"Peter Dutton's destructive messaging to people smugglers needs to stop because the only people that he's helping are those criminals who benefit from what is basically a trade in human misery."
Australian Border Force Commissioner Michael Outram has hosed down claims about a cut to the agency's funding, which the coalition claims has left the nation vulnerable.
He insisted federal funding had reached its highest levels since the agency was set up.
Former immigration officials have warned politicians to be careful with their rhetoric, saying it could lead to more boat arrivals.
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