But Ms Ardern told reporters in Wellington her government had already made its standing offer to take in 150 detainees to Nauruan authorities - only to be turned down.
"We've talked directly, through various channels, with the government of Nauru about that offer, as we have the Australian government. The government in Nauru has continued to point out they wish to work directly with Australia," she said, adding the offer still stood.
"Really, it's now beyond our own capacity to deliver on it."
World Vision New Zealand director Grant Bayldon says the children are living in sub-standard conditions.
Kelly Nicholls from the Refugee Council of Australia said there was a deep concern for all those detained offshore, and for children in particular.
"Worryingly, in recent months, there has been an escalation of reports of children suffering 'resignation syndrome' where they aren't leaving their beds and they've stopping eating, drinking, talking - even going to the toilet," she said.
Since 2013, New Zealand has had on the table an offer to relocate 150 asylum seekers from Nauru and Manus Island in Papua New Guinea - with the Ardern government ramping up the push.
Australia has repeatedly declined, citing concerns it would be used by people smugglers to lure more asylum seekers onto boats by advertising New Zealand as a backdoor.
A deal with the United States has been preferred and relocations are ongoing, although critics say new US immigration restrictions mean many detainees will not be able to be relocated there.
Australian Labor on Monday penned a letter to Home Affairs Minister Peter Dutton calling for him to accept the New Zealand offer, joining a chorus of charity groups calling for the children to be brought to Australia.
Nauru is next month hosting the annual Pacific Islands Forum.
Ms Ardern said the detention issue would likely be raised at the meeting.