"He killed my daughter ... and now he is living in New Zealand, free to do what he wants. I am absolutely furious."
Prime Minister John Key, speaking to reporters after attending an Apec summit in Manila, said he was unable to confirm speculation about what the flight's passengers had been convicted of.
"I don't have the individual details...but there are a broad range of people. Whatever the case is, we are comfortable that we have the best protections we practically can."
Mr Key said that included legislation passed under urgency this week, enabling deportees to be monitored by authorities in the way they would be, had they served jail time in New Zealand.
"Whether they [murderers and serious offenders] are part of the 12 or not, inevitably at some point they will be, because as we know there are people in that category in amongst the 585 that could be deported in the next wee while."
The detainees were all from the Christmas Island detention centre in Australia and arrived just after 10am.
Most have appealed Australia's decision to deport them for their crimes but would appeal from New Zealand, police said.
Police Superintendent John Tims said the operation went "really smooth" yesterday.
Mr Tims didn't comment on whether it was necessary to cuff the detainees, but said police were committed to ensuring the safety of detainees and of the public.
Eight of the offenders had supervision orders and all offenders had DNA samples and fingerprints taken.
Corrections northern commissioner Jeanette Burns said the offenders would be monitored closely and police and Ministry of Social Development staff would help them settle into the community.
Corrections provided transport for the offenders and housing for some of the deportees. Others would stay with family members.
Labour's Corrections spokesman Kelvin Davis said the detainees needed support if society was to integrate them.
"If they don't have food, accommodation and the other basics, they could fall back into crime, which is the last thing we want." Mr Davis didn't think it was necessary for the public to know where the deportees were going or what they'd be doing.
"The last thing they need is the public pointing at them. They've done their time in Australia. They're entitled to privacy."
Christmas Island saga
• Non-Australian citizens who have served a prison sentence of one year or more are being deported, potentially affecting up to 1000 New Zealanders.
• NZ detainees are being kept in detention centres in Nauru, Manus Island and Christmas Island either waiting for deportation or for the outcome of an appeal.
• Some detainees have complained about their treatment, and rioting broke out at Christmas Island following the death of an asylum seeker.
• Detainees have been told they can return to NZ, and an agreement has been made with Australia to speed up the appeals process.
