Allies of Jeb Bush and John Kasich are engaging in a full-fledged ad war, with super-PACs supporting the two Republicans releasing scathing TV commercials against each other on New Hampshire airwaves this week.

New Day for America, the outside group backing Kasich’s presidential campaign, is going up with a 30-second spot that calls out Bush for “desperately slinging mud” in the nomination contest. Right to Rise USA, which supports Bush, is calling Kasich “wrong on New Hampshire issues.”

Bush’s well-funded allies have spent millions attacking rivals in New Hampshire. Kasich has been targeted in mailers for his decision to expand Medicaid in Ohio and for his record on guns. Right to Rise has also slammed Marco Rubio in TV ads for missing Senate votes, and compared him to a weather vane on immigration.

New Day's anti-Bush ad, first obtained by Bloomberg Politics, will start airing on Friday in New Hampshire, said a person familiar with the group's plans who asked not to be named. It comes as Kasich, Bush, and other establishment-style candidates fight for second place behind front-runner Donald Trump in the Feb. 9 primary—and a ticket out of the Granite State.

The tone of the ad targeting Bush contrasts with the message coming from Kasich's campaign itself: that it's avoided the circular firing squad of Bush, Chris Christie, and Rubio while the Ohio governor wages a more optimistic campaign. Until now, the group’s negative spots have focused primarily on Trump.

The anti-Bush ad will replace one contrasting Kasich’s record as governor with the fiscal problems in New Jersey Governor Chris Christie’s state, the person said. It begins with gray footage of a dirt-drenched man, slouching in a field and wearing a “Jeb!” campaign button. “Jeb Bush once stood tall,” booms the narrator. “Before his campaign sank like a rock and he started desperately slinging mud on fellow Republicans. That’s not presidential, Jeb.”

As the music brightens and color returns, the commercial shifts to Kasich’s record, touting his cuts to Ohio taxes and state spending, along with his other economic accomplishments in the swing state. “That’s conservative,” the spot concludes, “and that’s presidential.”

YouTube: New TV Ad: "Mud"

Right to Rise showed Thursday it was simultaneously planning its own line of attack, putting out an ad targeting Kasich. “Where do you line up with John Kasich on the issues?” begins the spot, titled “Quiz.” The ad calls out the Ohio governor for expanding Medicaid, closing an Air Force base, and voting for “massive defense cuts.” It also questions Kasich’s fiscal responsibility as governor, one of the backbones of his presidential bid.

The Right to Rise ad went up on television in New Hampshire markets Thursday, Paul Lindsay, a spokesman for the super-PAC, said. “John Kasich, wrong on New Hampshire issues,” the ad concludes.

YouTube: Quiz

—Michael Bender contributed to this article. 

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