That's in line with a long-held policy, also supported by Labor, that no asylum seekers who come by boat will ever be granted permanent residency.
Dozens of asylum seeker families with children have been transferred in recent weeks, with many coming to Adelaide. The government is reportedly planning to get the remaining 38 children off Nauru before the end of 2018.
Source: Supplied/Kids off Nauru
Some of the people held on Nauru have already been found to be genuine refugees, while others have been refused or still have pending applications.
Regardless, none will be allowed to settle in Australia.
"That is the case and our policy hasn't changed," Mr Dutton told Sky News on Thursday.
"We've said very clearly that we don't want boats to restart; people are not going to settle here permanently."
It is understood 38 children of asylum seekers remain on the island.
Once medical support has been provided in Australia, non-refugees will be made to go back to their country of origin.
Refugees will be sent to the United States or resettled in other countries, Mr Dutton said.
A future Labor government would also block the asylum seekers from ever permanently settling in Australia.
"We support offshore processing and regional resettlement and that these people should be resettled," opposition immigration spokesman Shayne Neumann told ABC radio.
"Labor supports third country resettlement arrangements and we ask the government to consider the New Zealand offer."
Repeatedly asked whether children would be sent to Nauru in the future, Mr Neumann would only restate Labor's support for offshore processing and third-country resettlement.
Mr Dutton says there is increased "chatter" among people smugglers being intercepted by authorities and now is not the right time to be sending refugees to New Zealand because it will entice other asylum seekers.
Human Rights Law Centre advocacy director Daniel Webb plans to launch legal challenges to keep the children in Australia once they arrive but says the government is finding ways to get them to return.
Mr Dutton says people who pose a security risk will not be allowed into the Australian community, even if their child is being treated.
Additional reporting by AAP