Asked if the government knows where they are, Home Affairs Minister Clare O’Neil said its focus in managing the mandatory impact of the court’s decision was community safety.

“Yes, we do know where those people are,” she told Seven’s Sunrise program on Wednesday.

Last week’s decision by the High Court forced the government to release 80 immigrants in detention after ruling their indefinite detention – with no other country willing to take them – was illegal.

“Those crimes and those people are absolutely despicable,” the minister said.

“I’m raising three children in this country and I can tell you that if there was anything in my power to keep these people in detention, I would absolutely do it.”

Ms O’Neil said the government was releasing people under “the strictest possible visa conditions”.

This includes notifying authorities about their location, in-person daily reporting and restrictions on working in certain types of industries.

“It includes us continuously monitoring things like social media and email addresses and phone numbers and the like,” she said.

The Australian Federal Police commissioner has briefed his state and territory counterparts about the decision and a joint operation with the Australian Border Force has been established to co-ordinate their release.

Asked why the government didn’t have legislative or regulatory frameworks in place to deal with the issue, Labor minister Anika Wells said the High Court was yet to hand down the reasons for its decision.

“So for us to capture and make sure this doesn’t happen again, we need to know the reason before we draft any legislative or regulatory measure for the house,” she told Nine’s Today show.

Opposition Senator Jane Hume argued courts made decisions “all the time” that overturn or override government decisions.

The government had taken its eye off the ball because they knew the court’s decision was coming and were unprepared, she told Seven.

“Now we have 80 very dangerously, potentially, offenders out in the community,” she said.

Ms O’Neil said Senator Hume’s reasoning was “garbage”.

“The idea that it is open to the Australian government to simply legislate away a High Court decision is not the way our Constitution works,” she said.

Immigration Minister Andrew Giles has said the government sought prior advice about its options depending on a variety of outcomes of the court’s decision and continued to look at “all regulatory and legislative options”.