"I have an expectation that we will have the support from our coalition and our support partners on that."
A waka-jumping bill would ensure a party's proportional representation in Parliament, if an MP left a party.
Ardern said the discretion in the bill for party leaders to manage their MPs should make it amenable to both NZ First and the Greens.
The bill is expected to have a high threshold for expelling an MP. One suggestion was to have at least two-thirds of caucus support before an MP could be kicked out.
But the Greens have said little on the issue since the internal email was made public 11 days ago. The following day, co-leader James Shaw said he needed more information when asked about possible horse-trading over the bill.
Last week a party spokeswoman said the party had no comment. She confirmed this again this evening, when asked for a response to the Prime Minister's expectations of Green support for the bill.
The Greens can oppose government legislation as part of its confidence and supply arrangement with Labour. But the same agreement also binds the Greens to act in good faith and allow Labour to comply with its agreement with NZ First, which specifies passing a waka-jumping bill.