Ohio Gov. John Kasich's presidential campaign has chosen to spar with Texas Sen. Ted Cruz's team rather than challenge Donald Trump.

Kasich's team has charged that a vote for Cruz is a vote for Democratic presidential candidate Hillary Clinton, while Cruz's side has said that a vote for Kasich in upcoming primaries would benefit Trump.

Trusted Leadership PAC, a super PAC formed as an extension of several pro-Cruz groups, made a $500,000 ad buy in Wisconsin featuring radio and television advertising targeting Kasich.

"The John Kasich playbook: holding for a last second shot at blocking out the grassroots," a narrator says in a TV and radio ad. "But that's classic John Kasich. Millionaires working side-by-side with George Soros are bankrolling his super PAC, while Kasich votes against the Second Amendment and expanded Obamacare in Ohio, costing taxpayers billions. So given John Kasich's liberal record, it's no surprise his campaign isn't rebounding. Because John Kasich won't play in Wisconsin."

Soros himself does not appear to be directly bankrolling a pro-Kasich super PAC. But Scott Bessent, a former chief investment officer at Soros Fund Management who reportedly left Soros at the end of 2015, donated $200,000 to Kasich's supporters in 2015 according to records from the Federal Election Commission.

In response to the Cruz's supporters ad, Kasich's communications director Mike Schrimpf labeled Cruz "Lyin' Ted," adopting a label from Trump. The Kasich campaign's chief strategist John Weaver also pounced on Cruz, and tweeted on Tuesday that the Texas senator has "0 friends."

Kasich, who calls himself the 'Prince of Light and Hope,' publicly reprimanded Weaver when he attacked Trump on Twitter in 2015. He has not made any similar response to his campaign's decision to battle Cruz.

The governor has yet to intervene in the feud between his campaign and Cruz's supporters, but a pro-Kasich super PAC has decided to enter the fray. New Day for America filed a complaint with television stations in Wisconsin alleging the pro-Cruz super PAC's ad about Kasich is "false, misleading, and deceptive."

It remains to be seen whether Kasich will join his campaign in attacking Cruz. The Ohio governor, who has said he's not sure it's his "purpose" to become president, will hold one public campaign event in New York on Wednesday. His Republican competitors are stumping in Wisconsin, the location of the next GOP nominating contest.