A government minister has claimed parents prefer to pay a "modest amount" for children's food at a holiday club rather than have the label of a free school meal.
The Manchester United star launched a new petition last week urging the government to end child food poverty and called for vouchers to be distributed for October's half-term break and at Christmas.
It comes after Marcus, from Wythenshawe, forced the government into a spectacular U-turn with his campaign to provide free school meals during the summer holidays.
But the Prime Minister's spokesman said his success the first time will not be repeated, insisting: "We are in a different position now."
Speaking on Tuesday, Mr Zahawi said Universal Credit is available to support hard-pressed families and suggested that research from holiday clubs shows that parents prefer to pay a small sum for food.
He told BBC Radio 4's Today programme: "We've put over £9 billion into Universal Credit to help exactly those families that need that help, and we continue with the policy of holiday clubs."
The minister said research from a holiday club pilot scheme "demonstrates that families didn't just want the meals, although they valued the meals, they didn't like the labelling of them being free, they actually prefer to pay a modest amount, £1 or £2, but they valued the additional focus on exercise and on reading fun books and so on through the holiday".
Labour is set to force a Commons vote on the extension of free school meals to eligible children following its refusal last week.
The political party will table a motion calling on the Government to continue directly funding free school meals over the holidays until Easter 2021 to "prevent over a million children going hungry during the coronavirus crisis".
"Over a million children are at risk of going hungry over the holidays without access to free school meals. It is essential the Government provides this support urgently," shadow education secretary Kate Green said.
"We gave the Prime Minister the chance to change course, but he refused to do so. Now his MPs must decide if they want to vote for their constituents to get this vital support or if they will leave families struggling to put food on the table."
The Welsh Labour Government has already pledged to provide free school meals during the holidays until Easter next year.
And the parliamentary petition started by Rashford, has garnered around 300,000 signatures since being launched.
The 22-year-old footballer, who has been made an MBE for his services to vulnerable children, will see his petition debated by MPs under Parliamentary petition guidelines tomorrow (Wednesday).
However, Downing Street has shown reluctance to extend the scheme, with a spokesman indicating last Thursday that ministers would not provide free school meals to children in England during the Christmas break.
A Number 10 spokesman said: "It's not for schools to regularly provide food to pupils during the school holidays."
"It’s also not for food banks to feed millions of British children but here we are. 250% increase in food poverty and rising... This is not going away anytime soon and neither am I..."