Former Vice President Dick Cheney waded into a spat between his daughters, Liz Cheney and Mary Cheney, who is openly gay, saying that Liz's kindness to her sister shouldn't be used to "distort" her position supporting "traditional marriage."

One day after the two sisters appeared to take their disagreement public, Cheney and his wife, Lynne, issued a statement defending their daughter Liz, who is running for Senate in Wyoming.

"Liz has always believed in the traditional definition of marriage," the Cheneys said in a statement today. "She has also 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," they added.

The statement made no mention of Mary Cheney, 44, or her wife, Heather Poe.

READ: Liz Cheney Says She Is 'Not Pro-Gay Marriage'

Liz Cheney, who is challenging the Republican incumbent Sen. Mike Enzi of Wyoming in 2014, said on Fox News Sunday that she and her sister "disagree" on the issue of gay marriage.

"I do believe it's an issue that's got to be left up to states," Liz Cheney, 47, said. "I do believe in the traditional definition of marriage."

The comment prompted Mary Cheney's wife to issue a bruising statement on Facebook, which suggested that her sister-in-law welcomed their relationship privately.

"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 wrote on Facebook Sunday. "To have her now 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."

Poe's statement was quickly endorsed in a separate statement by Mary, who has two children.

Poe and Cheney married in 2012, and Dick Cheney has been publicly supportive of same-sex marriage since 2009.

But Liz Cheney, locked in a Senate primary with Enzi, has sought to run to the sitting senator's right flank.

The Cheney parents suggested, however, that the family rift over the issue existed long before the Senate bid by Cheney, who has five children.

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