The Child Poverty Action Group is calling for smaller classes in low-decile schools and higher pay for their teachers.
In a report published on Thursday, the group says 285,000 children live in poverty and governments are morally obliged to do more to help them.
The Government already gives low-decile schools more funding than others, as well as support for breakfasts and health care, but the report says it should go further.
It says decile 1 to 4 schools should provide free breakfasts and lunches, after-school and holiday clubs, and social and health services for the wider community.
The report says the Government should reduce class sizes in decile 1 to 4 schools, even if that means raising the number of children in high-decile classrooms.
Education Minister Hekia Parata said on Thursday a free breakfast programme is available to all schools, but most have not taken it up because they do not need it.
Ms Parata said it is up to schools to decide how many children are in each classroom and low decile schools can use their extra funding to reduce class sizes if they want to.