The Liberal Democrats have accused the Department for Education of "going rogue" by briefing against Nick Clegg.
The deputy prime minister has announced primary schools in England will get an extra £150m for new kitchens and dining rooms, to cope with the roll-out of free meals for infant pupils next year.
This would be part-funded by an £80m education underspend, Mr Clegg said.
But, after an education official told newspapers this was not the case, a Lib Dem spokesman accused them of "lying".
Details of funding to allow schools to build kitchens and expand dining rooms will be included in Thursday's Autumn Statement.
The £150m comes is on top of £450m set aside in 2014/15 and £635m in 2015/16 to fund the free lunches.
Under the government's plans every child in an English infant school will be eligible for a free school dinner, which is expected to save parents about £437 per year, per child.
Mr Clegg said: "From the start of the next school year, every single infant school pupil will be able to sit down to a free school lunch."
The £150m meant the government was "making the sums add up" and schools would not be "left out of pocket", he added.
Mr Clegg said universal free lunch provision would "bring children together from different backgrounds".
The cost was to be made up of £70m in new funding from the Treasury and £80m taken from unspent Department for Education (DfE) maintenance budgets, he added.
But the Guardian and Sun newspapers are reporting that the DfE informed them this shortfall did not exist.
However, a senior Liberal Democrat spokesman launched an attack on the Whitehall department, telling the BBC: "The DfE should stop whining and deliver. The DfE are going rogue. This has been agreed at the highest levels of government. It has been agreed by the chancellor."
He added: 'The DfE are hostile to ideas which are not their own. They are lying if they say the money isn't there. There is an underspend which will go partly to free schools, partly to school meals.
"The deputy prime minister wants the DfE to row back, and get with the rest of government and back this innovative policy."
A survey of local authorities conducted by the Children's Food Trust, published last year, found that about a quarter of primary schools did not have their own full food-production kitchen.
A Children's Food Trust spokesman said: "If we want more children eating in our canteens, schools have got to have the kitchens, equipment, dining room space and systems they need serve them well.
"With the right support some schools are already in a good position to get ready to serve more meals next September, but for others, capital funding for new facilities or refurbishment is going to be absolutely essential."
The trust said it wanted to see "more detail of how this funding will be allocated".
Russell Hobby, general secretary of the National Association of Head Teachers, said: "Free school meals are a good idea, but we need money to build the facilities that will be needed to provide them."
Proposals for free school lunches were first mooted in an independent review of school food, published in the summer.
For Labour, shadow education minister Lucy Powell said: "David Cameron and Nick Clegg scrapped Labour's plans to extend free meals for school children on taking office.
"Now they talk about helping with school meals, but in reality this Tory-led Government will have taken up to £7 billion a year of support away from children by 2015."