WASHINGTON — The public war of words over same-sex marriage between former Vice President Dick Cheney’s daughters escalated Sunday when Mary Cheney and her wife sharply criticized Liz Cheney for expressing clear opposition to gay marriage during a national television interview.

The back-and-forth was the latest round of a public split that has intensified in recent months. It comes as Liz Cheney is immersed in a heated campaign for the U.S. Senate in Wyoming, where her views on same-sex marriage have come under great scrutiny. It is also yet another instance of the Cheney family’s views on marriage becoming enmeshed in politics.

In an appearance on “Fox News Sunday,” Liz Cheney reiterated her opposition to same-sex marriage, telling host Chris Wallace that she disagrees with her younger sister, Mary, a lesbian who married her longtime partner, Heather Poe, in 2012.

“I love Mary very much. I love her family very much. This is just an issue on which we disagree,” Liz Cheney said.

That prompted a swift rebuke from Mary Cheney and Poe, who took to Facebook to voice their disapproval in strikingly personal terms.

“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,” wrote Poe. “To have her now say she doesn’t support our right to marry is offensive to say the least.” Mary Cheney shared Poe’s message on the social-networking website, adding: “Liz — this isn’t just an issue on which we disagree — you’re just wrong — and on the wrong side of history.”

In August, the spat spilled into public view after Liz Cheney said she is “strongly pro-life” and “not pro-gay marriage.” In response, Mary Cheney wrote on Facebook that while she loves her sister, she is “dead wrong on the issue of marriage.”

The current dust-up between Liz and Mary Cheney is not the first time someone in their family has attracted attention for remarks on gay marriage. Dick Cheney also has drawn scrutiny. He endorsed state-sanctioned gay marriage in 2009, saying in remarks at the National Press Club in Washington that “people ought to be free to enter into any kind of union they wish, any kind of arrangement they wish.”

As vice president in 2004, he appeared to put some daylight between himself and then-President George W. Bush, who supported a constitutional amendment to ban gay marriage.

Liz Cheney’s views on various issues have come under an increasingly bright spotlight since July, when she declared her campaign to unseat Sen. Mike Enzi, R. The primary campaign has turned contentious, with Dick Cheney lobbing barbs at Enzi and Liz Cheney confronting charges from critics that she is a carpetbagger who bought a home in Wyoming for political purposes.

Liz Cheney’s position on marriage also has become an issue in the campaign. A conservative super PAC released an ad in October casting her as insufficiently conservative on the matter. The commercial pointed to her opposition to a constitutional amendment banning gay marriage and her support for a State Department decision to extend benefits to same-sex couples.

On Sunday, Liz Cheney reaffirmed those positions, even as she repeated her opposition to same-sex marriage. “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,” she said.

While Liz Cheney has shown signs that she can compete with Enzi (she outraised him during the last fundraising quarter), she still faces a very tall task in trying to defeat him. Recent polling commissioned by the American Principles Fund, the group that ran the ad slamming Liz Cheney on marriage, showed Enzi holding a 52-point lead.

The primary election will be held in August 2014. The winner is expected to coast to victory in the general election, because of Wyoming’s heavily conservative tilt.