The free school meal entitlement was recently extended to post-primary pupils and independent schools, which will benefit an additional 15,000 pupils from September next year.
Mr Hazzard called for this to be extended to all school children.
"It is important that children are able to have a healthy meal during their time at school," the south Down MLA said.
"While welcoming the Minister's commitment to date on the issue I am asking him to investigate extending the free school meal system to all children attending school.
"This would bring equality to the system and ensure that every child would get at least one substantial meal during term time."
Many children were going to school without a proper lunch due to families being unable to either supply a packed lunch or pay for school meals.
Chris Hazzard, Sinn Féin
SDLP Education spokesperson Sean Rogers said that the Department of Education must recognise the challenges being faced by working families when it considers ways of increasing the uptake of free school meals.
"In recent years many families have fallen into the poverty trap - they hold down jobs, they work hard and yet they struggle to meet many of their bills," the south Down assembly member said.
"The working poor make a tremendous contribution to our society and deserve to be supported, in this case when it comes to their children.
"We need to support people who want to work and who greatly enhance our society by the contribution they make in the workplace. Losing a free school meal entitlement could make the difference of whether people return to work or not. I believe that we should aim to have free school meals for all Key stage one pupils."
The retired teacher added: "I was keen to put forward today an amendment to the motion which reflected the need to focus on nutrition and to recognise the challenges being faced by working families in the current economic climate."
We must not underestimate the important contribution which a healthy, nutritionally balanced school meal can make to a child's overall health and well-being, to learning and cognitive development and, in turn, to academic performance.
Education Minister John O'Dowd
DUP Chairman of the Education Committee Mervyn Storey MLA criticised the focus on free school meals as "the only method of addressing educational underachievement".
"Efforts to extend the entitlement of Free Schools Meals to those who are eligible particularly in controlled schools are to be welcomed. However, it is a false premise that in doing so educational attainment will be improved," he commented,
"This, as we have seen in the proposals to change the Common Funding Formula, would lead to massive disparities in how our schools are funded.
"Any policy change should be informed first and foremost by the needs of children. It should also be based on evidence from research and the experience of teaching professionals."
Meanwhile, Education Minister, John O'Dowd called on all families entitled to free school meals to take up their entitlement.
He revealed during the Stormont debate that one in five children eligible for free school meals do not avail of them.
Speaking after the debate, the Minister said: "The significance of free school meals must be seen in the context of my Department's overarching goals - 'to raise standards' and 'close the performance gap, increase access and equality'.
"Free school meals support the Programme for Government commitment to tackle disadvantage and close the gap in educational attainment between the least and most deprived communities.
"The particular challenges faced by pupils from lower income backgrounds in accessing, participating in and benefiting from, formal education are well documented and we should not underestimate the impact this can have on children's learning and development, on their educational attainment and ultimately on their lifetime opportunities."
The Minister continued: "Whilst there have been continued improvements in performance over recent years, there still remains too large a gap between pupils from socially disadvantaged areas and those from more affluent areas.
"Too many families are not accessing the support they are entitled to, I therefore urge parents who think they might be eligible to contact their Education and Library Board for advice."