National leader John Key has invited Helen Clark to join him on a visit to McGehan Close, suggesting it might convince her to reconsider her belief the "underclass" is diminishing.
But the Prime Minister has declined the offer, saying it might be a unique experience for him to visit such communities, but it is a regular part of her work programme.
Mr Key identified the Owairaka street in Auckland in his state of the nation speech as an example of one of a number where "helplessness is ingrained, a dead end, a place where rungs on the social ladder have been removed".
He cited it as evidence of what he claims is a growing underclass.
Labour hit back, with Helen Clark saying it was a strange time to make a speech about the growing underclass, as it was in fact decreasing in numbers.
The Government has released facts and figures to back up its case - as has National.
As the battle for hearts and minds continued, Mr Key said yesterday: "I find it a staggering response from the Prime Minister that she is denying there is an underclass."
The party had been deluged with emails and phone calls disagreeing with the Prime Minister's view.
"I intend to visit McGehan Close, I intend to visit some of the decile one schools in Auckland and I intend to visit some of the sports clubs in South Auckland where they are turning away people because they can't afford to pay for the sports.
"I welcome the Prime Minister if she wants to come with me on those visits. We can go together and if she doesn't, I'll go on my own. If she doesn't recognise there's an underclass that's growing ... she's welcome to that opinion, but I don't think New Zealanders share her view."
Helen Clark said through a spokeswoman that "the Prime Minister is a regular visitor to low-decile schools and communities and doesn't require his company. However she recognises that it may be a unique experience for him."
Mr Key was speaking from Gisborne where National MPs have gathered for a three-day caucus retreat.
He said Gisborne had not been selected because of its socio-economic problems.
But the party recognised there were significant and complex issues in Gisborne that had to be addressed, including gang problems.
Education Minister Steve Maharey said Mr Key's speech "shows he has failed to grasp the facts about what's going on in the country or the progress of the last seven years".
"He is trying to paint a picture of growing social unrest at a time when social outcomes are improving dramatically in this country. His willingness to mislead on these issues shows that he doesn't understand what is happening in New Zealand and that he has no new policies to offer.
"He needs to look at the facts. Maori unemployment is down by two-thirds, we have achieved the lowest unemployment in the OECD, a record 2.1 million New Zealanders are in work and we have seen the longest sustained growth in our country's history.
"Against this, we've seen major improvements for the lowest income New Zealanders, the cost of housing for people on low incomes has fallen dramatically, 61,000 children have been lifted out of poverty, and we have the lowest recorded crime in a generation."
Mr Maharey said Mr Key had offered no solutions to the tough social issues he raised.
Mr Key rejected those criticisms yesterday, saying he'd offered some solutions, but had also outlined a work programme which would deliver more answers.
Mr Key said the caucus retreat would resolve National's new position on the Maori seats and might resolve its stance on the Maori Party's foreshore and seabed bill.
On the seats, he said he favoured that they be abolished. "It's just really the question of timetabling. In the last election, we had a position that they would be abolished immediately if we won 51 per cent of the popular vote. I suspect the caucus might change that position and give a definitive timetable."
Under an earlier National policy, the party said it would only abolish the seats if Maori agreed.
He had harsh words for suspended Rakaia MP Brian Connell, despite having chatted to the MP when he turned up to listen to Mr Key's speech in Christchurch.
Mr Connell has claimed to have a number of caucus supporters pushing for his return.
Mr Key told the media in Christchurch that he intended to have a discussion with Mr Connell but said yesterday: "I wouldn't read too much into that."
* The number of Kiwis living in severe hardship has risen by 3 per cent between 2000 and 2004.
* Violent crime involving youths aged 14-16 rose 27 per cent between 1996 and 2005.
* 43 per cent of school leavers from low-decile schools have no qualifications, says the Education Ministry; 30,000 pupils are truant from school on any given day.
* Established child abuse cases have more than doubled since 2000, says CYF.
* One in four children are dependent on income-tested beneficiaries.
* Incomes for the poorest households have increased in real terms since 1999. Working for Families means families earning less than $35,000 will effectively pay no tax by 2008.
* Recorded crime has continued to decline from the early 1990s, from a peak of 1322 crimes per 10,000 population in 1992 to 994 in 2005.
* Child poverty rates fell from 27 per cent to 21 per cent in the three years to 2004.
* The cost of visiting a family doctor has fallen by half.