She said the circumstances had changed since the last time the offer was made - by English in February. "It is now an acute situation that Australia is dealing with."
Australia's concern in the past has been that refugees will settle in New Zealand and then move to Australia but Ardern said there were ways to deal with that.
"I don't think that should stand in the way of the offer."
In 2016 former Prime Minister John Key ruled out any moves that would have meant refugees taken by New Zealand were barred from Australia, saying it would have effectively created "two different classes of citizenship" in New Zealand.,
That US deal was agreed to by former President Barack Obama and the cause of a testy phone conversation between Turnbull and US President Donald Trump, who was unhappy Turnbull demanded he stick to the deal.
The two leaders will head to the Vietnam next weekend for the APEC Summit and also discussed the Trans Pacific Partnership. Ardern wants to re-negotiate to try to get an exemption for New Zealand from investor state dispute resolution processes that allow corporations to sue governments.
She said New Zealand and Australia had agreed on a 'side letter' for an exemption to the ISDS between the two countries - a common feature of the Closer Economic Relations process. The other 10 countries would remain a matter for negotiations, but she said New Zealand was not the only one concerned.
Ardern's plea to Turnbull to reconsider a policy to charge New Zealanders living in Australia the same tertiary fees as international students also fell on deaf ears.
Turnbull said while he understood the reaction in New Zealand, it was up to Australia to determine its policies in such areas.
"We respect each others' rights to lead and govern our own nations." He would not be drawn on whether he was concerned about an escalation in tit-for-tat policies.
Ardern said she would retaliate if Australia went ahead with those plans -especially given Labour's plans for three years of free tertiary education.
"What I've highlighted to the Prime Minister today is we have quite an expansive plan around tertiary education which will improve its accessibility.
It's only fair that if New Zealanders in Australia find they are incurring higher fees that we would make sure we respond by at least making sure our system is fair and equitable in the response that Australia citizens studying in New Zealand would experience."
Turnbull began the press conference by talking about the shared military history of New Zealand and Australia - and Ardern said the deployment of New Zealand troops to Iraq to work alongside Australian troops training Iraqi soldiers and security forces was also raised.
Labour had opposed that deployment and Ardern said she would decide on the future of that deployment when the current term ended in November next year.
"I'm not going to predetermine that, I've always said we'll look at the circumstances we find ourselves in at the given time. It is a complex conflict, things could change dramatically between now and then."
