New Cabinet Minister Andrea Leadsom has been branded "ignorant" after saying it would be sensible not to employ a man to look after children in case they are a paedophile.
Lib Dem leader Tim Farron said the remarks were so "stupid" that Prime Minister Theresa May should fire her.
Mrs Leadsom, who was appointed Environment Secretary after she quit the Tory run-off and allowed Mrs May to become party leader without a membership vote, insisted parents needed to be cautious when dealing with childcare.
"As an employer we're not, let's face it, most of us don't employ men as nannies, most of us don't. Now you can call that sexist, I call that cautious and very sensible when you look at the stats.
"Your odds are stacked against you if you employ a man. We know paedophiles are attracted to working with children. I'm sorry but they're the facts," Ms Leadsom told The Times.
Mr Farron said: "Andrea Leadsom has let yet another of her masks slip. These remarks are stupid, ignorant, and not ones any minister should be making. Over the last day Theresa May has shown she is willing to relieve ministers of their duties and she must do so again now.
"It is inconceivable that somebody who holds such offensive, ignorant views should be sat around the Cabinet table."
Labour shadow minister Jon Ashworth said: "This is an extraordinarily offensive statement from the new Environment Secretary. Andrea Leadsom should apologise immediately and the Prime Minister should also distance herself from these comments."
The Prime Minister's official spokeswoman said Mrs May had confidence in the Minister, adding: "These were personal views that were expressed, and she, as in Andrea Leadsom, has said that she employed a male nanny for five years, and doesn't think that men, or fathers, shouldn't be nannies."
A spokeswoman for Mrs Leadsom said the Minister had employed a male nanny and "was not saying that men are unsuitable as nannies."
The interview with Mrs Leadsom was conducted last week when she was still a contender for the Tory crown.
It follows the publication of earlier extracts in which she appeared to suggest being a mother made her better placed to be prime minister than Mrs May because she had a "very real stake" in the future of Britain.
Mrs Leadsom's views on childcare are out of kilter with society, according to a survey conducted by the Pre-School Learning Alliance of 1,200 mothers and fathers cited by the newspaper.
The survey found that 97.9% were happy for men to work with children aged between three and five in day nurseries, and 89% were fine with men working with children under three.