LONDON — A dispute erupted Saturday in the contest between the two women vying to become Britain’s next prime minister after one of them seemed to suggest in a newspaper interview that being a mother would make her a better leader than her rival, who does not have children.

The controversy over the remarks is the latest twist in a fierce campaign to succeed David Cameron as the leader of the governing Conservative Party and prime minister.

After losing last month’s referendum over whether Britain should remain in the European Union, Cameron said he would resign in the fall. The final two contenders to succeed him are Theresa May, the home secretary, and Andrea Leadsom, the energy minister.

Saturday’s dispute arose after The Times of London quoted Leadsom, who is a mother of three, as saying in an interview that having children meant she had “a very real stake’’ in Britain’s future. May and her husband do not have children.

According to the newspaper, Leadsom said that while May “possibly has nieces, nephews,’’ she herself had “children who are going to have children’’ who would be directly affected by what happened after Britain left the European Union.

Though her words do not appear to be in dispute — the newspaper released an audio recording of part of the interview — Leadsom reacted angrily to the presentation of her comments, and to the newspaper’s front-page headline: “Being a mother gives me edge on May — Leadsom.’’

In a Twitter post, Leadsom described the newspaper’s article as “truly appalling and the exact opposite of what I said,’’ adding, “I am disgusted.’’

Leadsom later said that her comments had been taken out of context, and that she had been asked repeatedly about being a mother and had said she did not want the issue to be part of the race.

“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 to be in any way a feature of the campaign,’’ she said.

“I want to be crystal clear that everyone has an equal stake in our society and the future of our country,’’ she added. “That is what I believe, and it is what I have always believed.’’

The leadership contest had already produced claims of treachery and betrayal, mainly involving the justice secretary, Michael Gove. Gove had first abandoned his friend Cameron to join the Leave campaign, then unexpectedly announced his candidacy for the top post, undermining the prospects of Boris Johnson.

Gove was eliminated from the contest on Thursday when Conservative lawmakers whittled down the field to May, 59, and Leadsom, 53. They will seek the support of 150,000 party members who will choose the winner in September.

In the recording released by The Times of London, Leadsom says she is sure May “will be really, really sad that she doesn’t have children, so I don’t want this to be ‘Andrea has got children, Theresa hasn’t’ — do you know what I mean — because I think that would be really horrible.’’

Leadsom goes on to add: “But genuinely I feel being a mum means you have a very real stake in the future of our country, a tangible stake.’’

The journalist and commentator who conducted the interview, Rachel Sylvester, defended her article, saying she was “baffled’’ by Leadsom’s reaction.

May posted a message on Twitter, saying, “Yesterday, I launched my clean campaign pledge, and invite @AndreaLeadsom to join me in signing it — TM.’’