The group, reportedly from Pakistan and Bangladesh via Indonesia, were found near a Âremote Indigenous community near the former West Australian church mission of Beagle Bay on Friday morning.
Operation Sovereign Borders commander Rear Admiral Brett Sonter issued a statement on Friday evening concerning the risks of public comment concerning the nation's security regime.
The mission of the military-led border operation remained the same as it was when established in 2013," Admiral Sonter said.
"Protect Australia's borders, combat people smuggling in our region and, importantly, prevent people from risking their lives at sea.
"Any alternate narrative will be exploited by criminal people smugglers to deceive potential irregular immigrants and convince them to risk their lives and travel to Australia by boat."
Questioned by journalists in Melbourne on Saturday, Mr Dutton said his experience as home affairs minister told him there was "no question about the fact Operation Sovereign Borders is not supported by the ... government.
"I know exactly how these people smugglers work," he said.
"They will react to a weak prime minister and to a weak minister. If they see vulnerabilities, they will exploit them, and that's exactly what has happened here."
Mr Albanese said he had spoken with current home affairs minister Claire O'Neill and been been briefed by Admiral Sonter.
"Our position on Operation Sovereign Borders is very clear and people who attempt to arrive here by boat will not settle here," he told reporters in Newcastle.
"I do say for people in public life to have a look at the very clear, strong and unequivocal message sent by Rear Admiral Sonter last night in the very clear statement that he made.
"We do not seek to politicise national security issues and it is unfortunate when any politician seeks to do so."
Push to respond to Mr Dutton's assertion he had not been tough enough on the issue, the prime minister said: "That says more about him than anything else."
A High Court decision in January to release 149 immigration detainees who had no prospect of being deported had already put Labor under pressure, with the opposition slamming the government's handling of the case.
More than two dozen have been re-arrested and charged since being freed, including for visa breaches.
Of the seven people accused of Commonwealth offences, three are in custody and four are on bail.
