LONDON (Reuters) - Andrea Leadsom, the junior minister seeking to become Britain's next prime minister, apologized to her childless rival over remarks which suggested she had a greater stake in the country's future because she was a mother.

Leadsom's comments, published in a newspaper interview on Saturday, caused an uproar and led to harsh criticism from supporters of Theresa May, the interior minister who is the favorite to replace David Cameron.

"I've already said to Theresa how very sorry I am for any hurt caused and how that article said completely the opposite of what I said and believe," Leadsom told the Daily Telegraph newspaper.

Leadsom was little known nationally before becoming a prominent figure in the campaign for Britain to leave the European Union but remains an outsider to succeed Cameron who said he would step down after Britons voted to leave the bloc on June 23.

Leadsom, a devout Christian, accused the Times of "gutter journalism" after it published an interview in which she said: "I feel being a mum means you have a very real stake in the future of our country, a tangible stake."

It prompted lawmakers in the ruling Conservative party to describe the comments as "vile" and "insulting". Leadsom told the Telegraph in an interview on Monday the row had left her in tears feeling under attack, and said she had been guilty of naivety.

"I absolutely said, what I specifically said, is that motherhood should not play a part in the campaign. I was pressed to say how my children had formed my views," she told the Telegraph. "Having children has no bearing on the ability to be prime minister."

(Reporting by Michael Holden; editing by Guy Faulconbridge)