Actor Sam Neill has called on Bill English to immediately take in Rohingya refugees who are fleeing worsening bloodshed in Myanmar.
Neill has tweeted English urging him to take in "many" refugees from "the most desperate circumstances", adding, "do the right thing Bill".
That plea comes after the Green Party in Australia called on the Turnbull government to take in 20,000 Rohingya refugees in an emergency intake similar to that set up after the violence in Syria.
Australian Greens leader Richard Di Natale said the state-led persecution of the Rohingya minority was worsening, with entire villages destroyed.
The United Nations' human rights chief has described the security operation targeting Rohingya Muslims in Myanmar as seemingly a "textbook example of ethnic cleansing".
High commissioner Zeid Raad Al Hussein urged Myanmar to end the "cruel military operation" in Rakhine state.
He said the situation couldn't be fully assessed because the Myanmar Government had refused access to human rights investigators. However, he said the UN had received "multiple reports and satellite imagery of security forces and local militia burning Rohingya villages, and consistent accounts of extrajudicial killings, including shooting fleeing civilians".
The Rohingya are a stateless mostly Muslim minority. Myanmar, which has a Buddhist majority, denies citizenship to more than 1 million Rohingya, despite the group living in Rakhine state for generations.
The UN says more than 300,000 Rohingya Muslims have fled to flood-hit Bangladesh since violence erupted late last month.
The Myanmar military claims it is responding to attacks by Rohingya militants and says it is not targeting civilians.
De-facto Myanmar leader Aung San Suu Kyi, who was awarded the Nobel Peace Prize in 1991, has come under criticism recently for failing to speak up for the Rohingya.
National last year announced that New Zealand's annual refugee quota would rise from 750 to 1000 in 2018 - the first increase since the quota was established in 1976.
The Greens want the quota increased to 4000 within six years, with an additional 1000 taken by NGOs.
Labour wants the quota to hit 1500 over three years.