The government "can't guarantee" that everyone eligible for 15 hours free childcare from September this year will be able to get a place.
The government announced a year ago that free childcare would be expanded so "thousands more parents won't have to choose between a career and a family".
From April this year, eligible working parents of two-year-olds will be able to get 15 hours of childcare support, and from September, these 15 hours will be extended to parents of children aged nine months to three years.
Asked about whether every eligible parent will be able to take advantage of the scheme, Education Secretary Gillian Keegan said the government was hoping this would be the case but couldn't guarantee it.
Speaking to Sunday Morning With Trevor Phillips, she said: "You know what you can't do Trevor, which I think you probably know is guaranteeing something in the future that you're not in control of all the bits.
"But what I will say is we are working to make sure that that offer, which I know parents are absolutely desperate for and I know our government is the only government that is determined to deliver it, but to make sure that we can deliver it. I've delivered many things here in my career."
Ms Keegan added that "deliverability has been at the heart" of the project, which is why it is being rolled out in stages.
The current goal from the government is that by September 2025, all eligible working parents with children aged nine months and up will be able to access 30 hours of childcare a week.
Under repeated questioning of why she cannot promise a place for every parent, Ms Keegan said Trevor Phillips was "trying to pick on semantics".
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The education secretary said she was being asked to "personally guarantee something on behalf of, you know, thousands, tens of thousands of businesses that are working there to grow the capacity and to make sure that we've got the people in place".
Ms Keegan said the government was "very confident" it will deliver on the scheme, and that it is "working flat out" to ensure places for children on the previously promised schedule.
"This is the biggest expansion of childcare in our country's history, and that's the plan, and we will stick with the plan, and I am determined that we will deliver it," she added.
Currently, working parents who earn the equivalent of 16 hours at the national minimum wage and make less than £100,000 in net income per year can get 30 hours of free childcare for offspring aged three to four.
Bridget Phillipson, Labour's shadow education secretary, responded to Ms Keegan's interview by saying: "The education secretary has made it clear.
"There are no guarantees that parents will receive their new childcare hours.
"This was a pledge without a plan - another broken Tory promise."