They're expected to hold bilateral talks at the APEC summit in Da Nang, Vietnam later this week after forming a special connection in their first skype conversation.
Speaking to the press on Sunday, Turnbull said he was focussed on Australia's refugee deal with the U.S. and wouldn't consider New Zealand's offer until after it was finalised.
Numerous men say they are too afraid to resettle in alternative accommodation and are refusing to leave the detention centre, which is also a Papua New Guinea (PNG) naval base.
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 made the offer to resettle refugees in 2013, but has been repeatedly knocked back by both Labor and Coalition governments.
Asked what that meant for Ardern's request to take 150, Turnbull said "we are not taking it up at this time".
Prime Minister Turnbull said that the Government intends to complete its arrangement with the United States, which will see 1250 refugees resettled, before it pursues any further arrangements with different countries.
"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".
"We of course do not have the circumstances that Australia is operating under, but we also can not ignore the human face of what Australia is dealing with as well".
Earlier today, a government backbencher broke ranks and said Australia should consider accepting NZ help.
Mr Turnbull's decision not to accept the offer may prolong what Greens leader Richard Di Natale has called a "humanitarian catastrophe" on Manus Island.
"It's a hard problem but we should not rule out any particular solution".
The last food packs were distributed on Sunday.
It was hoped a final agreement could be reached when world leaders meet next week but Japanese officials say attempts at renegotiation could cause the new TPP-11 proposal to collapse.