The meeting comes as roughly 600 asylum seekers on Manus Island have been left without power, food and water in an attempt by the government to encourage them to seek refuge on the island proper.
"We've had some really good discussions, we've covered a lot of ground", Mr Turnbull said.
Mr Turnbull ignored calls from the opposition and even a member within his own party to take the offer, saying he would first pursue a deal with the Trump administration to resettle 1250 refugees.
Turnbull had said that Australia was pursuing a deal with the United States to take more than 1000 refugees from Australia before he considered other offers.
"The agreement with the U.S. would lead to a substantial number of refugees being resettled", she said.
"We have an arrangement with the United States where a substantial number - 1,250 - can, subject to the USA rigours vetting, be resettled in the United States".
Ms Ardern's relationship with Australia has been controversial since her election with deputy PM Julie Bishop labeling the 37-year-old New Zealand leader "untrustworthy".
Australia withdrew from the Manus Island centre on Tuesday, following a PNG court ruling that the centre was unconstitutional.
"Of course, there would need to be conditions", Shorten said.
A federal government backbencher, Kevin Andrews, today broke ranks to support sending refugees to New Zealand to help end the stand-off on Manus Island.
"Yes, the United States are going to accept some of these people but there is still a large number there."
"We have serious concerns about the welfare, safety and wellbeing of the roughly 600 men who remain in the accommodation compound, who are too frightened to leave", spokesman Rupert Colville said.
Senator Di Natale said New Zealand had a more compassionate approach to refugees.
"They have said they are prepared to shelter some of these people and they are showing the decency and compassion that this Australian Government is so lacking".
"We are talking about people who have been attacked and assaulted in these camps, where women who have been raped have been denied terminations".