Sen. Ted Cruz refused to say Tuesday whether he would still back Donald Trump if the GOP presidential front-runner wins their party’s nomination, backing away from a firm pledge he made earlier in the campaign.

Mr. Cruz, whose coziness with Mr. Trump last year had pundits saying they were in the middle of a bromance, said that faded once the billionaire businessman began to turn nasty, and particularly in recent days when Mr. Trump has said he would go after Mr. Cruz’s wife.

“I’m not an easy person to tick off, but when you go after my wife, when you go after my daughters, that does it,” Mr. Cruz said at a town hall hosted by CNN in Wisconsin Tuesday night.

He accused Mr. Trump of being behind a thinly sourced story last week in the National Enquirer tabloid that reported Mr. Cruz had engaged in affairs with a handful of women. The story aggregated rumors, and the only named source was Roger Stone, an adviser to Mr. Trump, who said: “These stories have been swirling around Cruz for some time. I believe where there is smoke there is fire.”

Mr. Cruz also backed away from the pledge all of the candidates took last year to back the eventual nominee no matter who it is. Mr. Cruz ducked repeated direct challenges by CNN host Anderson Cooper to take a firm stand, saying instead that his goal now is to make sure he doesn’t face that choice.

“The answer to that is to beat him at the ballot box,” Mr. Cruz said.

Mr. Cooper, though, said Mr. Trump had made controversial statements about women and minorities last year, even as Mr. Cruz was praising him: “Sounds like you were engaged in a love fest,” Mr. Cooper said.

Mr. Cooper also pressed Mr. Cruz to explain his call for more police patrols in Muslim neighborhoods in the U.S. as a way of combatting the threat from terrorists. As an example, Mr. Cruz pointed to a discontinued program in New York City that the police commissioner there has said didn’t work. Mr. Cruz said the commissioner was under pressure from New York City Mayor Bill de Blasio, a Democrat and supporter of Hillary Clinton.

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