Ms Moroney said National had approached Labour "after the weight of public opinion convinced them to rethink its threat of using a financial veto to scupper the bill".
The Government Administration select committee has now delayed its report on the bill until February 28.
"I hope National MPs will use the summer break with their families to reflect on how Labour's proposal to extend parental support will help mums and dads bond with their babies in the crucial early months", Ms Moroney said.
Finance Minister Bill English said National hadn't changed its position on the bill but now understood it "may be worth looking at".
National has previously said it was interested in the idea, but didn't see it as affordable.
However, Mr English said the select committee had now done detailed work to come up with a version that wouldn't be vetoed.
"We just haven't had the opportunity to look at the detail of where they've got to."
Delaying the date at from which the extension would apply was a possible concession that may persuade National to support the bill he said.
"The original bill just cost too much too soon to be acceptable or workable. Costings would be one issue where the Government would want to see where the committee's got to."
"The bill now looks substantially different and may be worth looking at."
- By Adam Bennett of the New Zealand Herald
