Andrea Leadsom has appeared to suggest being a mother makes her a better choice for prime minister than Theresa May.
Leadsom is quoted by The Times as saying that being a parent gives her an edge in the race to succeed David Cameron because it showed she had a "very real stake" in the future of the country.
The comments - just days after May, the home secretary, spoke about how she and her husband were affected by being unable to have children - have sparked a huge backlash, with some Tories questioning her suitability to be prime minister.
One Tory backbencher told ITV News that Leadsom's comments were "vile", while another said she should now drop out of the leadership race.
Leadsom has accused the newspaper of "gutter journalism", saying she is "disgusted" by the story and wants a retraction.
The Times used the headline "Being a mother gives me edge on May - Leadsom" and said the 53-year-old had got "personal in her ruthless campaign" to become prime minister.
Leadsom told Times journalist Rachel Sylvester: “Genuinely I feel that being a mum means you have a real stake in the future of our country, a tangible stake,” she said.
The mother-of-three said 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”.
Leadsom also said May must be "really sad" not to have children and that she did not want to capitalise on it as to do so would be "really horrible."
But asked to contrast herself with the home secretary, Leadsom 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.”
Leadsom has demanded a retraction from The Times after claiming she had been misrepresented - despite the newspaper publishing a full transcript and audio of the interview.
Speaking later outside her home in Northamptonshire, Leadsom said she was "disgusted" by the front page.
She insisted she believes "everyone has an equal stake in the future of our society".
After The Times story was published, May repeated her invitation for Mrs Leadsom to join her in signing a pledge to run a clean campaign.
Business Minister Anna Soubry led Conservative criticism of the remarks, saying it proved Leadsom "was not PM material".
David Cameron refused to comment on the row.
Speaking at a Nato press conference in Poland, the current prime minister said he would not make any comment on the contest to pick his successor.
Foreign Secretary Philip Hammond dismissed suggestions that politicians needed to be parents to be good prime ministers.
He pointed to May's depth of experience compared to her rival.
"Most of my colleagues [foreign ministers] do not know Andrea Leadsom, have never heard of Andrea Leadsom," he said at the Nato summit.
"Many of them do know Theresa May from the joint meetings of interior ministers and foreign ministers we have had in response to dealing with CT [counter-terrorism] issues in the European Union. She is a known quantity and her reputation goes before her."
Leadsom's supporters have jumped to her defence.
"I'm afraid this is an attempt, I think, by a paper that has declared for the other candidate to smear Andrea," Armed forces minister Penny Mordaunt told BBC Radio 4's Today programme.