Leadsom, a 53-year-old mother of three, told the Times of London that being a mother "means you have a very real stake in the future of our country."
May, 59, is the current frontrunner in the race to become the next British prime minister in September after David Cameron resigned following the E.U. referendum. She recently spoke about not being able to have children.
Leadsom and May were selected as finalists this week in the Conservative Party leadership contest, meaning that Britain will have its first female prime minister since Margaret Thatcher left 10 Downing Street in 1990.
Leadsom has challenged the newspaper and demanded to see a transcript of the interview. She tweeted a cover of Saturday's edition of the Times of London that reads "Being a mother gives me edge on May - Leadsom" and said that it was "truly appalling and the exact opposite of what I said. I am disgusted."
But the Times has stood by its story, and its reporter Rachel Sylvester released an audio of the transcript on the BBC on Saturday morning. The quality of the audio wasn't great - the interview was conducted at a noisy cafe at a train station - but there was no mistaking what Leadsom had said.
Here it is:
"I don't really know Theresa very well. But I am sure she will be really, 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, but genuinely I feel that being a mom means you have a very real stake in the future of our country, a tangible stake. You know, she possibly has nieces, nephews, you know, lots of people, but I have children who are going to have children who will directly be a part of what happens next."
Sylvester also told the broadcaster that, in a wide ranging interview, she asked Leadsom what were the main differences between herself and May. She said Leadsom responded "first of all she said economic competence, because of her background in the city," - Leadsom is a former bank executive - "and then she said family. She said her kids were a huge part of her life, she also had brothers and sisters."
May is married and doesn't have children. She rarely talks about her personal life, but recently spoke about not having children.
May told the Mail on Sunday last week: "Of course, we were both affected by it. You see friends who now have grown-up children, but you accept the hand that life deals you. Sometimes things you wish had happened don't, or there are things you wish you'd been able to do, but can't. There are other couples in a similar position."
On Saturday morning, Leadsom was trending on social media.
"I am childless. I have nieces and nephews. I believe I - like everyone else - have a very real stake in our country, " offered one poster.
"Leadsom apparently thinks the c, 20 percent of women who won't have children are second-class citizens. Tories steering back to 1950s?" said another.
Leadsom countered via Twitter:
"Truly appalling and the exact opposite of what I said. I am disgusted."
© 2016 The Washington Post
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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