Treasury was still working through how many households that package would help after admitting its initial assessment that it would lift 88,000 out of poverty was overstating its impact.
Ardern said once that was known Labour would be able to assess what else was required.
She conceded the Government books did not allow for a second round of support of the same scale, but the first package would have a "significant impact" and there were other less costly measures that could be taken to reduce deprivation.
That included targeted support for material hardship, such as heating.
As well as income, one of the measures for child poverty will be the index of material hardship – a list of 17 items which the Ministry of Social Development uses to assess how many households lack basics such as healthy food, clothing, accommodation, heating and transport. That includes whether children have more than one pair of shoes and the ability to afford heating.
Ardern is seeking National Party support for the bill, saying child poverty has always been a driving force and she wants any gains to continue after her own time in office.
"What this bill is saying is that we are not afraid to be held to account. We should set high standards, particularly when it comes to children and wellbeing.
The thing that makes a big difference are the policies we put in place and so that goes well beyond this bill. But this bill is the foundation for the future work I want every government to do."
National leader Bill English said his caucus was yet to decide whether to support it and would consider it over the next two weeks but did not believe the legislation was needed.
He said he shared the desire to reduce child poverty. However, the public service was already using the measures Labour proposed and the decision to abandon the public services targets National had used would be detrimental. He said those targets had helped National reduce the number of children in material hardship by 85,000 over the last five years.
"By getting rid of these targets, the Government has thrown away the very tools to attack these drivers of poverty. The Government's new proposals are so high level and general that they refer to no one in particular, and no one will be held responsible for any lack of progress."
Ardern said the decision not to include specific targets in the legislation was deliberate. She had initially wanted to include them but was advised not to if she wanted political consensus.
"I wanted to do them separately because the question as to whether you support this bill at the moment has nothing to do with our targets – it's whether you support the ambition of holding yourself to account in future over child poverty."
She believed it would be supported. "I think Kiwis have a really good sense of what feels fair and what feels right in a country like New Zealand. Families who don't have enough income to put decent food on the table and to ensure their kids have the right clothes for school isn't right in a country like New Zealand."
She said the targets and actions to achieve them would be included in the child wellbeing strategy which was required under the legislation.
