A row has erupted after Conservative leadership candidate Andrea Leadsom was accused of suggesting that having children made her a better choice to be prime minister.
The Times quoted the mother of three as saying having children meant she had "a very real stake" in Britain's future.
She later said she was "disgusted" with the interview's presentation.
Times journalist Rachel Sylvester defended her article, saying she was "baffled" by Mrs Leadsom's reaction.
Mrs May, who has no children, has launched a "clean campaign" pledge and invited Mrs Leadsom "to join me in signing it". Her campaign team has declined to comment on the Times's story.
David Cameron also refused to comment on the row saying he was "playing no part" in the election and would say "absolutely nothing".
The Times headlined its front-page lead story: "Being a mother gives me edge on May - Leadsom."
It quoted the energy minister as saying Mrs May "possibly has nieces, nephews, lots of people.
"But I have children who are going to have children who will directly be part of what happens next".
Speaking outside her home in Northamptonshire, Mrs Leadsom said she was "disgusted about how this has been presented".
"In the course of a lengthy interview yesterday, I was repeatedly asked about my children and I repeatedly made it clear that I did not want this in any way a feature of the campaign," she added.
"I want to be crystal clear that everyone has an equal state in our society and in the future of our country.
"That is what I believe and it is what I have always believed... this campaign must at all times be principled and honourable."
In an earlier statement, she said the reporting had been "beneath contempt".
By BBC political correspondent Eleanor Garnier
We won't know the true impact of this row until the result of the leadership race is announced in September.
It is the Conservative Party membership that votes on who should be leader and there may well be some who would like their next leader and prime minister to be a mother.
But many others will say it doesn't matter at all and it shouldn't be used in any way to try to get ahead in the campaign.
That is why there has been such a huge reaction to Andrea Leadsom's comments - with senior Tories calling her remarks vile and demanding an apology.
Mrs Leadsom's team have told me they are putting in an official complaint to the Times and have asked the paper to print it.
It's clear she wasn't trying to be cruel to Theresa May but it has shown her inexperience and some say a lack of judgement so crucial if you want to be PM.
Ms Sylvester told the BBC the article had been "fairly written up" and she was "baffled" by Mrs Leadsom's "rather aggressive reaction".
"I asked her a very straightforward question... She raised Theresa May and the fact that she doesn't have children," she said.
"I asked her directly 'what are the differences between you and Theresa May?'.
"She said 'economic competence and family'... she clearly thinks that is a big selling point with her."
Ms Sylvester added that it was "accurate journalism" and she thought Mrs Leadsom was "naive to make that comparison and not think it would become an issue".
The Times, which backed Remain in the EU referendum, has previously backed Mrs May to become the next Conservative leader.
The pair will battle it out to become the next Conservative leader after two rounds of voting reduced the contenders to two.
After the second MPs' ballot, Home Secretary Mrs May finished with 199 votes and Energy Minister Mrs Leadsom 84.
Conservative party members will now decide the winning candidate, with the result due on 9 September.
What Mrs Leadsom said:
Rachel Sylvester: "Do you feel like a mum in politics?"
Andrea Leadsom: "Yes. So...
RS: "Why and how?"
AL: "So really carefully because I am sure, 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 being a mum means you have a very real stake in the future of our country, a tangible stake.
"She possibly has nieces, nephews, lots of people, but I have children, who are going to have children, who will directly be a part of what happens next.
"So it really keeps you focused on 'what are you really saying?'. Because what it means is you don't want a downturn but 'never mind, let's look ahead to the ten years', hence it will all be fine. My children will be starting their lives in that next ten years so I have a real stake in the next year, the next two."
Conservative leadership election
- Ballot papers sent out mid-August
- Ballot closes noon on 9 September. Votes will be counted electronically
- Members can vote by postal ballot or online
- "Qualifying party members" of more than three months' standing can vote (anyone who joined the party by 9 June)
- Spending limit set by Conservative 1922 Committee is £135,000
- Hustings to be organised across UK