Dutton had earlier warned New Zealand that it had to consider the trans-Tasman relationship, but last night his language was more forceful against the notion that Ardern may be giving boat people hope.
"It's a waste of money in my judgment," Dutton said, referring to the offer of $3 million.
"Give that money to another environment, somewhere where ... Indonesia, for example. We're the biggest donor into Indonesia for people who are displaced.
"I don't want hope being offered out to anyone that they're going to come to Australia. I don't want them rejecting the US position on the promise that maybe one day they'll go to New Zealand or somewhere else."
Today Australian Prime Minister Malcolm Turnbull took a softer stance than Dutton, thanking New Zealand for its offer to help.
"We thank them for the offer, they've kept it outstanding. But our focus is on completing the resettlement arrangements with the United States, which, of course, covers up to 1250 refugees."
After dealing with the US, he said taking up New Zealand's offer was a possibility - a stance he has held since his bilateral meeting with Ardern in Sydney almost two weeks ago.
"It's a possibility that could happen in the future but it is ... no near-term prospect at all."
Opposition leader Bill English has also cautioned Ardern not to push Australia too hard on the issue, given that Australia protects New Zealand by picking up boats that may be headed here.
He has questioned whether Ardern's repeated pleas for Australia to accept the offer was merely "making a show", given that Australia has not taken up the offer since then-Prime Minister John Key first made it in 2013.
Australia has expressed concern that any refugee arriving in New Zealand could then move to Australia, given the freedom of movement between the countries.
Earlier this week, Dutton confirmed that the refugees on Manus Island had been accused of 161 offences, including sexual assault, which had been referred to Papua New Guinea police.
About 370 men have refused to leave the detention centre on Manus Island. They have had limited food, water and power supplies since the centre was closed on October 31.
The humanitarian crisis has attracted widespread condemnation from the United Nations and human rights observers.