Wyoming Republican Senate candidate Liz Cheney on Sunday said that she disagreed with her own lesbian sister's desire for equal marriage rights.

Fox News host Chris Wallace pointed out to Liz Cheney on Sunday that her married sister, Mary, had called her "dead wrong" on the issue of marriage equality.

"I love Mary very much, I love our family very much," Liz Cheney replied. "This is just an issue on which we disagree."

The candidate noted that she favored some rights for same sex couples.

"I don't believe we should discriminate against people because of their sexual orientation," she explained. "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 in their life insurance, there's no reason we shouldn't do that. I also don't support amending the Constitution on this issue."

"I do believe it's an issue that's got to be left up to the states, I do believe in the traditional definition of marriage," Liz Cheney added.

Update (3:00 p.m. ET): Mary Cheney and her wife, Heather Poe, responded to Liz Cheney's comments on their Facebook page on Sunday.

"Liz – this isn’t just an issue on which we disagree, you’re just wrong – and on the wrong side of history," Mary Cheney wrote, according to The New York Times.

“Liz has been a guest in our home, has spent time and shared holidays with our children, and when Mary and I got married in 2012 – she didn’t hesitate to tell us how happy she was for us,” Poe added. “To have her say she doesn’t support our right to marry is offensive to say the least.”

“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."