Workplace Relations Minister Iain-Lees Galloway says he is willing to work with the National Party to advance paid parental leave for partners - but not at the moment.
A lunch was held in Parliament today to celebrate the Government's first bill, currently passing through Parliament, which will extend paid parental leave to 22 weeks next year, and to 26 weeks from July 2020.
National justice spokeswoman Amy Adams is trying to amend the bill so that both parents can take some of the leave entitlement at the same time.
Former Labour MP Sue Moroney, who championed paid parental leave as an MP, was at the lunch and said the next step was "getting some exclusive partner leave" in place.
"Getting everyone in the family that attachment and bonding opportunity would be a wonderful next place to go to.
"Those are the sorts of flexibilities that I want to see all families have ... all families, all partners, all fathers."
Galloway has resisted National's amendment, saying that the current bill is about the bonding between babies and their primary caregiver.
But he told the crowd at lunch that he supported Moroney's proposal.
"I absolutely want to pick up the baton exactly as you describe, Sue ... I have already extended the invitation to the National Party for us all to work together on what the next steps are for paid parental leave.
"But today this is about completing this phase of the journey."
Mother Lisa Woods, who was at the lunch with her nine-month-old Zach, said having more paid parental leave would make a huge difference.
"When I had Zach, it really brought home to me how important it was. In those early months, the development is just profound.
"If you don't have that leave and the ability to do it, it's really hard."
She said her partner also took two weeks of leave when Zach was born, and it would have been great if he could have accessed paid parental leave as well.
"It's so hard at the beginning, learning how to look after a baby, and it's really important that the dads have that connection and build that bond, as well as the mum."
She said ideally there would be 26 weeks' paid parental leave for the primary caregiver as well as dedicated paid leave for the other parent.
Moroney told media that she supported National's amendment, and ideally wanted the Government to legislate for two weeks' paid leave for partners.
But she understood Galloway's reluctance to adopt National's amendment.
"[The current bill] has been through select committee twice. That particular provision hasn't been through a select committee and I understand their reasoning of wanting to get some more advice on that."
National's amendment had unlikely support from Labour MP Willow Jean Prime - who has two young daughters including three-month old Heeni.
"That is one of the most challenging times, as soon as Mum has given birth and I know in our own situation that was a time I really appreciated having my husband there."