Turnbull said Australia was working with the United States to try and get Manus Island refugees settled in the United States. That was the priority and then other options could be considered.
Earlier at the same press conference Ardern declared her Government would not make the offer to take up to 150 refugees to Papua New Guinea directly, given Australia was still considering it.
"The offer is still under active consideration by Australia. So there is no need to do so. I absolutely understand the priority being placed around the agreement with the United States," Ardern said.
"From New Zealand's perspective, we want our offer to remain on the table."
Today's meeting was the first between Turnbull and Ardern, and the Australian Prime Minister told reporters, "we have hit it off well and we will continue to do so". He then referenced Ardern's prior performances as a DJ.
"This did not come up in the talks," Ardern said.
"No, but I heard about this. And of course I made a rather feeble attempt at rapping on a television show recently so I don't know whether we can...," Turnbull said, before Ardern again cut in to say no joint act would be announced.
Turnbull noted Ardern was born in Hamilton, the same city where his own mother had lived. They had discussed that link today, Turnbull said, including his memories of "clambering over Maori pas and eating a very large quantity of feijoas".
Ardern said she had invited Turnbull to New Zealand to do some fishing.
Turnbull said the TPP, anti-terror efforts, threats to regional security including tensions with North Korea were all discussed. He told Ardern her understanding of the Pacific was "second to none", referencing her father Ross's placement in Niue as High Commissioner.
Most questions at the short media conference after the meeting focused on Manus Island.
More than 600 refugees have barricaded themselves in the mothballed detention centre, which closed on Tuesday.
Australia has in the past not taken up New Zealand's offer to take 150 refugees, because of concerns that once in New Zealand they would have the right to live in Australia, and that such deals could encourage people to make boat journeys.
Turnbull did not answer a question on whether any consideration had been given to accepting New Zealand's offer in such a way that could limit the refugees' ability to move to Australia in the future.
On the TPP, Ardern reiterated her Government's desire to renegotiate the Investor State Dispute Settlement (ISDS) clauses in the TPP trade deal. Those provisions allow foreign investors to take action against a TPP country if they believe it has breached its investment rules.
"We have discussed a side letter between New Zealand and Australia on ISDS clauses, which is something that we see as being mutually beneficial."
Turnbull was also asked about the deportations of New Zealand expats living in Australia who have cumulatively served 12 months or more jail time, and the possibility the children of expats could pay much more in tertiary fees. During the campaign Ardern threatened to shut Australians out of university here in retaliation if the same happened in Australia.
Turnbull said he respected the right of New Zealand to manage its own affairs, and "I know New Zealand respects our right to do the same on this side of the ditch".
Breaking ranks on Manus Island
Earlier, an Australian government backbencher broke ranks to support sending refugees to New Zealand.
More than 600 refugees have barricaded themselves in the mothballed detention centre, which closed on Tuesday.
"We should give consideration to what New Zealand is offering," former immigration minister Kevin Andrews told Sky News on Sunday.
"It's a difficult problem but we should not rule out any particular solution."
He acknowledged there were concerns about a New Zealand refugee resettlement deal establishing a pull factor for people making boat journeys or becoming a back door to Australia.
But Andrews said if a deal could be crafted to work around those issues it should be given thorough consideration.
- Additional reporting NZN
