Meanwhile Papua New Guinea Immigration Minister Petrus Thomas says it's no longer possible to restore services to the Manus Island detention centre, and has urged its inhabitants to leave.
Mr Turnbull thanked Ms Ardern for the offer, which was first made by former prime minister John Key, and said his Government remained focused on a refugee resettlement deal with the United States.
It comes as the standoff on Manus Island enters into its fifth day, with more than 600 refugees having barricaded themselves into the detention centre which closed on Tuesday.
New Zealand first said it would take 150 of the asylum seekers in 2013, but the offer has been repeatedly rejected by Australia, the BBC reported.
The issue was raised by Ms Ardern with her Australian counterpart Malcolm Turnbull in a meeting in Sydney on Sunday.
Ardern had said she could not ignore "the human face" of what Australia was dealing with.
Speaking to the ABC, Shorten said "Australia is not and must not be a resettlement option but it is [Prime Minister Malcolm] Turnbull's responsibility to work with other nations on resettlement options".
So far 54 refugees have been resettled in the US.
Mr Thomas also said the PNG government could not continue to bear the cost of watching over residents at the mothballed centre.
Opposition leader Bill Shorten has urged Turnbull to take up the deal, saying that it would not put "people smugglers back in business".
The stand-off at the Manus Island detention centre prompted Opposition Leader Bill Shorten to issue a statement on Friday, calling on Mr Turnbull to accept the offer, describing it as not dissimilar to the United States deal.
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.
"The reality is, we have an intractable problem at the present time", he told Sky News.