Mr English said a recent survey found that only 3 to 4 per cent of children were missing out on breakfast.
"I don't think it's correct that tens of thousands of kids are turning up without breakfast.
"There is no doubt that when they do, they are not in great shape to learn. We are willing to grapple with that problem without setting out to undermine the efforts and the sense of responsibility that most parents have for their kids."
His comments follow an outpouring of public support for the food charity KidsCan in two recent media campaigns.
KidsCan chief executive Julie Chapman said a fundraising day on More FM raised $100,000, and last Friday's "lunchbox day" on TV3's Campbell Live show raised $319,000.
On top of that, George Weston Foods increased its donations of Tip Top bread from 30,000 to 46,000 loaves a year, EaziYo offered to provide yoghurt, and the Trillian Trust pokie fund upped its ongoing grants to the charity by $200,000.
This week, Mrs Chapman emailed all 70 schools on her waiting list saying that food is now available.
"We think we will be able to almost completely eradicate the waiting list for food," she said.
The charity already feeds 4500 children a day at 220 schools, but estimates that it would need $3.4 million a year to meet the total need of 15,500 children a day, or one-eleventh of the 167,000 students in the country's 861 decile 1-4 primary and intermediate schools.
Initial results from a survey of those schools have found that 68.5 per cent say some of their students have experienced hunger this year "regularly" or "all the time".
KidsCan has put a proposal to the Government for it to pay $1.5 million towards a comprehensive national programme, with KidsCan raising the other $1.9 million required from corporate and public fundraising.
The charity already gets $150,000 a year from the Crown.
Mrs Chapman said Mr English's comments were "the strongest indication yet that he is prepared to do something".
The minister said the Government was also considering a proposal by Dr Wills' expert group for a "warrant of fitness" scheme to improve the quality of rental housing, along with other possible reforms such as relaxing planning rules for new housing.
"We are taking a great deal of interest in how that market is regulated, because if housing prices and rents rise, it's going to cost the Government a lot of money and put more people at risk of finding themselves in low-quality housing."
Mr English said the expert group had also put up "a pretty strong case" for passing on child support to sole-parent beneficiaries, but that needed to be considered alongside other possible approaches.
Revenue Minister Peter Dunne said the Government could not afford the $159 million-a-year cost of passing on all child support.
But he would talk to Dr Wills about how to make child welfare a greater priority under a new law reforming the payment system.
- Additional reporting: Andrew Laxon