Ardern reacted angrily to suggestions that her offer - first made by John Key in 2013 - was encouraging people smugglers.
Anyone who tried to put at risk vulnerable people's lives should come under the full force of the law, she told reporters in Manila covering the East Asia Summit.
"They must be stopped. New Zealand has played a role in trying to stop them."
New Zealand had worked with Australia for a number of years to stop people smugglers and would continue to do so.
She said the reported "chatter" among people smugglers eager to try to get to New Zealand was nothing new.
"I've been given no indication that that chatter ever stopped. We know it has been an ongoing issue."
The Courier Mail reported that Operation Sovereign Border had intercepted four boats heading to New Zealand carrying 164 people but it has no knowledge of whether it was recent or historic.
Former Prime Minister John Key revealed in 2015 that a steel hulled boat carrying 65 people had been intercepted on its way to New Zealand and it had been returned to Indonesia.
Ardern told reporters that the "passing" conversation with Turnbull was not a snub and that i was splitting hairs to suggest her talks with him weren't substantive because they weren't sitting down for a meeting.
But Ardern herself in Vietnam four days ago publicly signalled her wish for more "substantive" talks over New Zealand's offer to take
"National Party leader Bill English accused Arden of "making a bit of a show of putting pressure on Australia over Manus Island, knowing that Australia won't take up the offer".
He said the story of the boats heading to New Zealand was a sign of the "cost" of Ardern's position.
"We rely on the co-operation with Australia to ensure people don't head to New Zealand in these boats ... It's the Australian authorities that see them and turn them around."
Offshore processing centres for refugees were set up by Australia in Nauru and Manus Island, Papua New Guinea, to stop mass boat arrivals.
Over 400 in PNG are refusing to leave their detention centre for alternative accommodation in the Manus community after a court ordered it to be closed.
Meanwhile, Green Party foreign affairs spokeswoman Golriz Ghahraman, and a former refugee, said New Zealand should not be afraid of boat people trying to reach our shores.
"We are more open and it's something we can be really proud of because we are upholding our values and our law.
"People have a right to escape war and torture. We will process them if they are being persecuted and we will give asylum [if they are found to be genuine refugees]."
She accused Australia of "scaremongering".
