Ms Ardern is holding talks with the left-wingers this week as she mulls a power-sharing arrangement in New Zealand, where coalitions are common.

The re-elected prime minister doesn't need the Greens' support to form a government as Labour was handed a parliamentary majority in the October 17 election and can govern in its own right.

However, Ms Ardern said last week she was "interested in areas of co-operation where we can use the strengths that exist in their team for the benefit of the government and New Zealand".

The two parties met for around 90 minutes on Tuesday and plan to meet again on Wednesday.

Both sides have agreed not to discuss the contents of the meetings, placing a focus on the snacks shared during the talks.

"We saw an immediate upgrade in biscuits from Krispies to MallowPuffs, so a little bit more sugar and a little bit more cream," Greens co-leader Marama Davidson said.

"We've managed to progress discussions ... I can't divulge the actual content or the substance, but we're working hard and we are moving forward."

Pundits believe the Greens may be offered ministries outside of Cabinet as a reflection of their support for Labour during Ms Ardern's first term, when it was needed for government.

That would include the return of Greens co-leader James Shaw to the climate change portfolio, and could elevate Ms Davidson into an executive role.

"We're moving as fast as we can but forming a government is a complicated business and we have a lot to work through," Mr Shaw said.

Ms Ardern, who did not speak publicly on Tuesday, has signaled her intent to conclude talks this week.

A spokesman for the Labour leader said "conversations progressed well".

The Greens then need to take any deal to join the government to their membership, which must ratify the decision with a vote of over 75 per cent of party members.

The Labour leader intends to hand out portfolios - including the soon-to-be vacant deputy prime minister and foreign affairs roles - next week.

Australian Associated Press