Peters said the Iraq deployment was discussed, but New Zealand had not stated any position on a further deployment.
That would be discussed further when Australia's Prime Minister Malcolm Turnbull and PM Jacinda Ardern met in March.
Bishop said she would soon attend a meeting in Kuwait with Iraq's leader and expected to hear more then about what further assistance Iraq might seek.
New Zealand would be represented at that meeting.
New Zealand's deployment will end later this year and Australia's in 2019.
Bishop said what happened next would depend on Iraq.
"It depends very much what Iraq seeks from us. It will depend on the needs and requirements of other coalition partners."
She said Australia and New Zealand had collectively trained 28,000 soldiers and Iraqi security forces.
Peters said New Zealand had not had a definitive request from Iraq as yet so could not make a decision.
Manus Island
Bishop has given no signal that Australia will budge on allowing refugees from Manus Island to settle in New Zealand, saying there were many other options.
Bishop said they had discussed people smuggling and Australia's attempts to halt it through border protection.
New Zealand's offer to take 150 refugees has not definitively been rejected, but appears to be at the bottom of the heap.
Bishop said Australia was still working on re-settling refugees in the United States and there were other options beyond that. She listed those as PNG, Nauru or Cambodia.
Bishop was also asked about her statement that she would find it hard to trust a Labour Government and said that was behind her.
"Australia and NZ stands side by side on almost every issue of importance to our nations."
Ardern a hit with Bishop
Ardern's merino loafers were quite a hit with Australia's Foreign Minister Julie Bishop despite Ardern admitting they look like slippers.
Ardern has been wearing the Allbirds shoes a lot lately, including when she returned to Auckland last night and popped in to meet Bishop for the first time.
Bishop was at dinner at NZ Foreign Minister Winston Peters' private home in Auckland, which Bishop said showed the closeness of the relationship.
Peters said he had not done the cooking: "no, she deserves better than that."
Bishop said she and Ardern had discussed a wide range of matters and was asked if she had noticed Ardern's shoes.
Ardern had put a slightly shame-faced mention of her casual shoes and jeans on social media after Bishop tweeted a photo of them together.
Bishop said "seriously?" When she was first asked if she had noticed the shoes but proceeded to say Ardern had explained she was in casual clothes because she had been at a party summer camp.
She said Ardern had told her the shoes were merino and NZ made and very comfortable.
"I had shoe envy at that stage."