Finance Minister Conor Murphy has pledged the money will be found to extend free school meal payments through the summer.
It comes after the Education Minister said he will ask for funding to cover the scheme through July and August.
The payments ensure around 97,000 children here, particularly from disadvantaged backgrounds, have continued to receive support even though many schools are closed due to the lockdown.
Northern Ireland is the only part of the UK not to extend the scheme over the summer.
Yesterday, in a U-turn, the UK Government announced a Covid summer school fund to ensure those who avail of free schools meals in England receive a six-week voucher, following a heartfelt plea by Manchester United footballer Marcus Rashford.
The striker, who has spoken of experiencing hunger as a child, penned an open letter to MPs after the Government said it would not award free school meals vouchers in England outside of term time.
Yesterday Prime Minister Boris Johnson praised Rashford's "contribution to the debate around poverty". Wales and Scotland have also announced similar free school meal extension schemes.
However, the local scheme that sees families receive a £27 payment every fortnight is due to stop at the end of this month, prompting MLAs to demand the Department of Education extend the policy.
First Minister Arlene Foster said she will be proposing the extension of the scheme, but said approval will be dependent on the necessary funding being found.
Education Minister Peter Weir had previously said his department did not have the money to extend the scheme, which has cost £19m, outside term time.
Last night Mr Weir said: "I am fully aware of the concerns that some children will go hungry over the summer period, especially this year when direct payments in respect of free school meals are due to end on June 30.
"I am currently considering options to cover the July and August period and will be making a bid for funding of just over £12m from the Executive's Covid-19 fund to provide a summer food scheme for those children who normally receive free school meals.
"This will form part of a wider paper on summer activities to be considered by the Executive when they meet on Thursday.
"This will include a proposal to extend the Education Authority's 'Eat Well Live Well' programme, which has been running for a number of months and is currently providing healthy breakfasts and lunches to over 3,000 vulnerable young people."
With Sinn Fein having also called for an extension, it is likely that additional financial support will be approved.
Mr Murphy tweeted: "I'm determined to identify the money necessary for this. Hope to bring proposals to Executive in near future."
Mrs Foster told the Assembly: "I am very sympathetic to ensuring that our young people have the certainty of at least one good meal per day over the summer months. And we know that that is a challenge for many families. And I know this is an issue the Deputy First Minister (Michelle O'Neill) also takes very seriously, and indeed, having spoken to the Education Minister, he is also very supportive.
"Doing well in education can be dependent on a range of different home, and indeed, personal factors, but we need to ensure that young people have the best possible opportunity to succeed too when they return to school, hopefully in late August/September.
"There are exceptional circumstance due to Covid-19 therefore I will be proposing to the Executive that meals continue to be provided to that cohort of children over the summer period this year, if the necessary finances can be secured.
SDLP South Belfast MP Claire Hanna insisted food banks across here will face increasing demands if additional funds are not allocated to extend meal payments.
UUP MLAs Mike Nesbitt and Robbie Butler yesterday tabled a motion for Stormont to introduce an equivalent scheme to the Government's summer school fund.
"Strikingly, Scotland, England and Wales have already said that they will continue with their support for those who receive school meals through the summer," said Mr Nesbitt.
Meanwhile, Victor Leonard, the chairman of the SuperCupNI tournament, described Rashford as "an inspiration to everyone."
The player was twice a winner with Manchester United at the international youth football competition.