The Energy Minister is quoted in the Times as saying that being a mother “means you have a very real stake in the future of our country” but insisted she was not trying to make it an issue in the Tory leadership election.
It follows May urging her rival to sign a pledge committing to a clean campaign.
Mrs Leadsom, who has two sons and a daughter, said being a member of a “huge family” was an important part of who she was.
The comments sparked an angry reaction from many on social media last night.
However she later said that the reporting of her comments was “beneath contempt” and that she expected the newspaper to retract the article and its headline.
The comments in The Times come just days after the Home Secretary spoke about how her and husband Philip were affected by being unable to have children.
The energy minister is quoted as saying: “I am sure Theresa will be really sad she doesn’t have children so I don’t want this to be ‘Andrea has children, Theresa hasn’t’, because I think that would be really horrible.”
Journalists from the Times posted sections of an interview transcript on Twitter.
In a highly personal interview with the newspaper, Mrs Leadsom said: “Genuinely I feel that being a mum means you have a very real stake in the future of our country, a tangible stake.”
Asked to contrast herself with Mrs May, she said: “I see myself as one, an optimist, and two, a member of a huge family and that’s important to me. My kids are a huge part of my life.”
Mrs May told the Daily Telegraph separately that she likes to keep her “personal life personal” but says that she and her husband “dealt with” the fact they couldn’t have children and “moved on”.
“I hope nobody would think that mattered,” she said. “I can still empathise, understand people and care about fairness and opportunity.”