Senior UK judges this month ruled Mr Assange can be extradited to the USA to face charges over his publication of confidential war documents.
His legal team, including New Zealand-based lawyer Craig Tuck, want Ms Ardern to make representations to US President Joe Biden or UK Prime Minister Boris Johnson to end the "politically motivated prosecution".
"This is something our prime minister could address by picking up the phone to president Biden or prime minister Johnson and saying, 'Hey, enough's enough. Let's bury the hatchet and not in Julian's head'," Mr Tuck told Radio NZ.
"Let's move on. This thing needs closure. There are issues of freedom, of kindness, of democracy (at play)."
The Australian's plight is not a hot-button issue in Wellington, though parliament is considering a private member's bill to further protect journalists from revealing their sources from court or police orders.
Mr Tuck said the 50-year-old Assange had recently suffered a stroke, and he feared for his health if extradited to America.
"It is arguably the most important human rights case on the planet," he said.
"Where is the New Zealand Labour party at? Where is New Zealand parliament at on this?
"(Assange) is a journalist. He's speaking the truth. He's speaking truth to power. He's suffered enough. This is really quite a perverse prosecution."
Also on Monday, independent Hobart-based MP Andrew Wilkie urged Australian Prime Minister Scott Morrison to intervene to support Mr Assange's case.
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