Peter Dutton has been publicly castigated for "irresponsible" comments about asylum seekers after triggering rare interventions from two border security chiefs.
A group of 39 men 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.
The opposition leader has since attacked the Albanese government as "weak and incompetent" on border protection and challenged its committment to the Australian Border Force.
"When Labor was last in government, the Rudd-Gillard period, they did take money out of border force ... they never see national security as a priority," he told Melbourne radio 3AW on Tuesday.
On Friday, when Mr Dutton raised similar concerns, Operation Sovereign Borders commander Rear Admiral Brett Sonter warned against "any alternate narrative" about the agency's capability, saying it could be exploited by people smugglers.
On Monday, Australian Border Force Commissioner Michael Outram made a rare public foray to hose down claims about the agency's funding levels.
He told Nine Newspapers federal funding was at its highest level since the agency was set up io 2015.
Prime Minister Anthony Albanese slammed Mr Dutton for "making things up".
"In his (Dutton) irresponsible comments, they can be seen as nothing other than encouraging this activity (people smuggling)," he told reporters on Tuesday.
"He needs to be held accountable for that."
Former immigration officials have also warned politicians to be careful with their rhetoric, saying it could lead to more boat arrivals.
Home Affairs Minister Clare O'Neil said the Nauruan government would be primarily responsible for the medical treatment of the men, 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 Radio.
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.
Asked how the asylum seekers were able to reach Australia's shores undetected, she said the country had a large border.
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.
"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."
Asked when the government would put forward the first application to re-detain someone under preventative detention, Ms O'Neil said she wouldn't "put a timeline on it".
"We're working through applications at the moment and just remember that that's only one of the layers of protection that our government has put in place," she said.
Laws were pushed through the parliament last year in response to a High Court decision which ruled indefinite detention was unlawful.
The home affairs minister said she didn't believe the legislation for preventative detention needed to be changed.
