But Cheney and his wife appear to be siding with Liz, and said in the statement that it is possible to be loving toward a lesbian sister and her spouse while not embracing the idea of their marrying.
"This is an issue we have dealt with privately for many years, and we are pained to see it become public," the parents' statement said. "Since it has, one thing should be clear: Liz has always believed in the traditional definition of marriage. 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."
Cheney is heavily involved in his older daughter's bid for the Senate seat in Wyoming and has been helping her to raise money for the race. The Cheneys appear eager to prevent the family feud from becoming an issue in the race.
The two sisters have not spoken since the summer, and Mary Cheney told the New York Times on Sunday she will not reconcile with Liz unless she changes her position on marriage.
Mary Cheney has kept up her advocacy on her Facebook page, responding sharply to one commenter on the page who urged her to be "lovingly tolerant" of her sister's position on same-sex marriage.
"This isn't like a disagreement over grazing fees or what to do about Iran," Mary Cheney wrote. "There isn't a lot of gray here. Either you think all families should be treated equally or you don't. Liz's position is to treat my family as second class citizens. That's not a position I can be 'lovingly tolerant' towards."