The prime minister "is committed to free school meals in England", an official spokesman told the BBC.
The coalition government introduced the meals a year ago for all pupils in the first three years of school in England.
But there has been speculation the meals are at risk, after Chancellor George Osborne demanded cuts of between 25% and 40% from unprotected budgets.
The spokesman said the prime minister had made the point that "it was in the manifesto, the manifesto words are very clear - we're proud of what we've done with free school meals".
The Conservative manifesto says: "We will support families by providing free meals to all infants".
The chancellor called for the cuts in July, as part of his spending review, due to be published in November.
The free school meals budget has cost about Â£600m each year, and there had been speculation over its future.
But the Department for Education has indicated that free school meals will be protected in the spending review.
"We believe that every child, regardless of their background, should have the same opportunities," said a spokesman.
"That is at the heart of what we are doing with school food.
"No child should be hindered because they are not eating a nutritious meal at lunchtime.
"We have provided significant financial support to schools to help them deliver universal infant free school meals.
"We have come a long way, and the new School Food Standards mean pupils of all ages are eating good food that sows the seeds for healthy eating for life."
At the weekend some 40 top health professionals signed a letter warning that scrapping the meals could harm children's health.
"It would be short-term thinking indeed for the government to cut the funding for universal infant free school meals," said the letter.
The National Association of Head Teachers called for "a swift and unequivocal statement" from government that it would honour its general election pledge to fund a meal for all infant children.
"That message could and should be delivered straight away," said NAHT general secretary, Russell Hobby.
"Schools signing contracts with catering companies this term can't afford to wait until the November spending review only to find out the policy has been changed."

A report said the force was inadequate at protecting vulnerable victims.
Surrey Police boss Nick Ephgrave said the force was good at preventing crime but this potentially came at the expense of investigations.
Inspector Zoe Billingham said Surrey showed a "commendably strong commitment to keeping people safe from harm".
She said the force had strong, mature neighbourhood police teams who worked well with councils, and neighbourhood officers had more training than in other forces.
But she said: "The way the force investigates more complex crime requiring specialist investigations is still not good enough.
"Many investigations that we reviewed were not of an acceptable standard and there were long delays in examining computers and mobile phones for evidence."
She said the force needed to improve its understanding of the threat posed by organised crime, improve its process for mapping those groups, and fully mobilise its neighbourhood teams in the fight against organised crime.
Mr Ephgrave, temporary chief constable, said the force was already tackling concerns by increasing resources to protect the vulnerable, and providing more training, better process and use of systems, and a culture change in how the force operated.
He said: "None of these things can provide an instant fix but together they are starting to deliver positive results."
A separate report by HM Inspectorate of Constabulary (HMIC) in December last year found Surrey Police's approach to protecting vulnerable people to be inadequate.
Surrey police and crime commissioner Kevin Hurley said changes were already in place, including a change in chief constable.
This month it emerged that Mr Hurley had considered seeking Ms Owens' dismissal as Surrey Police chief. She resigned last autumn to move to her new role as director general of the National Crime Agency
Mr Hurley said: "When we look at where the buck stops, it stays with the team manager."
But he said the force was already turning around, with reductions in robbery and burglary, improvements in violent crime and rape investigations, praise for the force's action on anti-social behaviour.
The BBC has approached Ms Owens for a comment. In a previous response, she said blame apportioned to her was "ill-considered and inaccurate".
"I was selected to my current role by the Home Secretary after a lengthy and thorough process and am now focused on leading the National Crime Agency in its fight to cut serious and organised crime," she said.
David Cameron has dismissed speculation free school meals for all infant children could face cuts.
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Surrey Police needs to improve how it investigates crime and tackles serious and organised crime, a government inspector has said.