"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 joint press conference in Sydney 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 term ended in November next year.
She said she would make that decision based on the best information available - and would not rule out a visit to Iraq herself to see the work of the troops.
"I will want to make sure I am fully informed before I make a decision. The best way to do that is to get as close to the deployment as possible."
Ardern said New Zealand's offer to take 150 refugees from Manus Island was still a possibility, despite a lukewarm response from Turnbull.
Turnbull had said that Australia was pursuing a deal with the US to take more than 1000 refugees from Australia before he considered other offers. Asked what that meant for Ardern's request to take 150, Turnbull said: "We are not taking it up at this time."
Ardern said the offer had not been rejected and remained on the table. "Whilst it has not been taken up immediately, the Prime Minister thanked New Zealand for the offer, acknowledged it and it is something that still remains in place."
Turnbull had defended the decision not to accept New Zealand's offer, despite one of his own backbenchers urging him to consider it.
He said the focus was on the deal to get the United States to take more than 1000 before other options were looked at.