A planeload of New Zealand detainees deported from Australia is due to arrive by the end of the week.
The 20 New Zealanders are the largest single group of detainees to return.
Justice Minister Amy Adams will introduce a bill to Parliament today that will subject those who committed serious criminal offences to mandatory monitoring. It is likely to be passed under urgency by this evening, or tomorrow at the latest.
Ms Adams said she understood some of those returning were serious offenders.
"We're concerned about every returning offender who poses a risk to New Zealand and this group, certainly from the indications I've had, contains some people with serious criminal histories."
Many of those returning have spent time on Christmas Island where there were riots last week.
"I couldn't say whether every one of them has, but certainly these are New Zealanders who have taken up the opportunity that was made available to them to come back to New Zealand while the completion of their appeals is carried out.
"And as you know we have no ability to deny them that, as New Zealand citizens that is their right."
Last week, Ms Adams gave out a list of crimes committed by some detainees which included manslaughter, armed robbery and aggravated assault.
Her bill would lead to greater oversight by authorities of those returning, she said.
"They will have an obligation to provide certain core information that we would expect of people who were arrested in New Zealand - fingerprints, name, details and the like.
"Depending on the length of their sentences, they will become subject to mandatory monitoring conditions and oversight and they will also be subject to any other conditions that the court sees fit to impose to manage the particular risk profile."
Labour Party leader Andrew Little said he was concerned about lack of scrutiny of legislation being rushed through Parliament today. Mr Little told Morning Report Labour had suggested she introduce two bills, one under urgency, and one that will go through the full process, with full public scrutiny - and he was waiting to hear back.