Former US Vice President Dick Cheney’s two daughters are locked in an open and very personal feud over equal marriage.

Liz Cheney, a candidate for the US Senate seat of Wyoming, told Fox News Sunday she believed in the “traditional” definition of marriage.

The remarks prompted her sister Mary Cheney, who is a lesbian and married, to post on Facebook: “You’re just wrong.”

“Liz – this isn’t just an issue on which we disagree – you’re just wrong – and on the wrong side of history,” she wrote after watching her sister state her view on Fox News.

Mary Cheney posted a quote from her partner, Heather Poe, saying that the elder Cheney sister “didn’t hesitate to tell us how happy she was for us” when they wed last year in Washington DC.

“Liz has been a guest in our home, has spent time and shared holidays with our children,” Ms Poe wrote. “To have her now say she doesn’t support our right to marry is offensive to say the least.”

Mary Cheney condemned her older sister in September for not supporting marriage rights for same-sex couples.

Dick Cheney himself said in 2011 “he didn’t have any problem with” same-sex marriage.

Mr Cheney and his wife Lynne released a statement today saying they had sought to deal with the issue privately “and we are pained to see it become public”.

They said their daughter had “always believed in the traditional definition of marriage” but “always treated her sister and her sister’s family with love and respect”.

Clearly aware of the risk that conservative hardliners would use that fact against Liz Cheney, they added: “Compassion is what is called for, even when there is disagreement about such a fundamental matter and Liz’s many kindnesses shouldn’t be used to distort her position”.

Mr Cheney, who served for eight years under former President George W Bush, has long been loathed by American liberals, but on the issue of equal marriage he has become an unexpected progressive, angering conservatives by announcing in 2000 that he would not oppose it.