Cabinet Minister Penny Mourdant admitted there "have been issues" with the Government scheme to provide food vouchers to low-income children.
Ms Mourdant, the Paymaster General, was responding to Newcastle North MP Catherine McKinnell, who told her the voucher system is "not fit for purpose".
The Govermment scheme is designed to help the 1.3m children who would usually be eligible for free school meals but cannot receive them because schools are closed during the lockdown.
Parents instead receive regular food vouchers worth £15 per child per week, which they can spend in supermarkets.
Teachers have to upload data onto a website before parents can apply for vouchers, but there are reports of staff waiting in hour-long queues just to log in.
There is also concern that parents who do not have access to the internet or are not confident using online services are unable to apply for vouchers, and they may not be able to receive them if they do have an email address.
The scheme is run by French corporate services group Edenred on behalf of the Department for Education.
Speaking in the House of Commons via video link, Ms McKinnell welcomed plans to step up testing for coronavirus, and tracing of those who have been infected.
She added: "It's just one of the issues that we need to get right before we can re-open schools.
"Headteachers in my constituency are really struggling to support vulnerable pupils, particularly with free school meal vocuhers, because the the system used by the government's chosen provider Edenred is just not fit for purpose.
"Will the Government urgently get a grip on this to ensure that at least our chuldren get fed?"
Ms Mourdant said: "I know that there have been issues with the voucher system which the Department for Educatio has been looking at."
She asked Ms McKinnell to send her details of specific problems in her Newcastle constituency.
