Image copyright Reuters Image caption Mary Cheney (centre) and Liz Cheney (right) watch their father take the oath of office for his second term in 2005

An argument between former Vice-President Dick Cheney's two daughters about gay marriage has gone public.

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

The remarks prompted her sister Mary Cheney, who is married to a woman, to post on Facebook: "You're just wrong."

The two sisters have reportedly not spoken in several months.

Mr Cheney himself said in 2011 "he didn't have any problem with" same-sex marriage.

Liz Cheney is campaigning to become the Republican senator for Wyoming. But first, she must oust the party's incumbent, Mike Enzi, from his seat. To decide the contest, a primary election will be held next August.

'Offensive'

Same-sex marriage has become an issue in Ms Cheney's campaign after she publicly declared she was not in favour of it.

To have her now say she doesn't support our right to marry is offensive to say the least Heather Poe, Liz Cheney's sister-in-law Q&A: Same-sex marriage in the US

But a group ran attack ads suggesting that she had previously voiced support for same-sex marriage rights.

When asked about her views, Ms Cheney told Fox News if "people are in a same-sex relationship and they want their partner to be able to have health benefits or be designated as a beneficiary on their life insurance, there's no reason they shouldn't do that".

But she added: "I do believe it's an issue that's got to be left up to the state. I do believe in the traditional definition of marriage."

But Mary Cheney - who worked on the re-election campaign on George W Bush, an opponent of gay marriage - took umbrage at her sibling's comments.

She posted on Facebook: "Liz - this isn't just an issue on which we disagree you're just wrong - and on the wrong side of history."

Heather Poe, Mary Cheney's spouse, responded on Facebook that "[Liz] didn't hesitate to tell us how happy she was for us" when they were married in Washington DC last year.

"To have her now say she doesn't support our right to marry is offensive to say the least," she wrote.

"I can't help but wonder how Liz would feel if as she moved from state to state, she discovered that her family was protected in one but not the other. "

When asked for comment on her wife's post, Mary Cheney told the New York Times she had believed Liz had always been "very supportive" of her relationship with Ms Poe.

But she said that now it would "impossible" for them to reconcile as long as the Senate candidate maintains her position.

Mr Cheney and his wife Lynne said on Monday their elder daughter has "always believed in the traditional definition of marriage".

"This is an issue we have dealt with privately for many years, and we are pained to see it become public," the Cheneys said in a statement.

They said Liz Cheney had "always treated her sister and her sister's family with love and respect, exactly as she should have done".

"Compassion 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," the family said.