"We want to get it to zero, but we have to be sensible about the way that we do it."
Labor had written to the Federal Government asking it to consider amendments to legislation that would pave the way for Australia to take up New Zealand's offer, he said, including guaranteed acceptance of the offer and the removal of all children and their families from Nauru to New Zealand.
"Let me say this, there are 13 children on Nauru at the moment who are involved in family groups - they are adults, mostly males within that family unit - that are the subject of adverse security assessments from the United States.
"The first question is, is New Zealand going to take those people when the United States has advised that that person, that individual in the family unit, is a risk to national security," Dutton said.
Labor wants a proposed lifetime ban on re-entering Australia to apply only to those refugees on Nauru resettled in New Zealand, not other countries.