On Friday, Cruz denied a story in The National Enquirer that accuses him of having several extramarital affairs, denouncing them as "garbage" and angrily accusing Trump and "his henchmen" of trafficking in "slime" and "sleaze."
The Texas senator told reporters in Oshkosh, Wisconsin, on Friday that the Republican presidential campaign has taken a "darker turn" in what is an escalation of the back-and-forth between the two.
Trump hasn't held a public event since Monday, and Cruz says the billionaire businessman is "hiding in Trump Tower" and campaigning via Twitter instead of meeting with voters.
Asked if he plans to vote for Trump should he win the GOP nomination, Cruz says, "I don't make a habit of supporting people who attack my wife and my family."
Trump denied that claim, releasing a statement that he knows nothing about the allegations on social media and in a supermarket tabloid that Cruz has cheated on his wife, Heidi.
The developments came a day after Cruz branded Trump a "sniveling coward" as the feud over their wives took a nastier turn.
After an earlier and vague threat to "spill the beans" about Heidi Cruz, Trump stoked the spat on Twitter when he retweeted side-by-side images of Cruz's wife, with an unflattering grimace, and his wife, Melania, in a gauzy, glamorous pose.
"No need to spill the beans," said the caption. "The images are worth a thousand words."
Ted Cruz, campaigning in Wisconsin, was livid.
"Leave Heidi the hell alone," Cruz said, speaking through reporters to Trump. "Donald does seem to have an issue with women. Donald doesn't like strong women. Strong women scare Donald."
Trump was set off this week when a group that opposes him released an ad before the Utah presidential contest raising questions about the propriety of Melania Trump becoming first lady. The ad showed a provocative, decade-old magazine photo of her when she was a model and before she married Trump.
Trump wrongly attributed the ad to the Cruz campaign and warned on Twitter: "Be careful, Lyin' Ted, or I will spill the beans on your wife!"
The lurch into personal territory normally off limits in campaigns came as an anti-Trump super PAC ran an ad in primary states that features women reciting derogatory comments made by the billionaire about women. The ad was produced by Our Principles, a group founded by a former Mitt Romney campaign adviser who is trying to help the Republican Party appeal to more women.
Trump has a substantial lead in the delegate chase for the GOP nomination. Cruz has a stiff challenge trying to catch him in remaining races and may only have a shot at the nomination if the contest spills into the summer convention.
Meanwhile, Democratic presidential candidate Hillary Clinton brushed aside speculation that her husband Bill recently made comments that were critical of President Barack Obama.
In a West Coast appearance earlier this month, former President Bill Clinton commented that his wife was best qualified to help America emerge from eight agonizing years. Hillary Clinton, in an appearance late Thursday on ABC's "Jimmy Kimmel Live," said that wasn't what her husband was talking about.
"It wasn't. It obviously wasn't," she said. "He nominated President Obama for his second term." Some construed Bill Clinton's comments as a shot across Obama's bow.
Hillary Clinton said her husband was referring, instead, to "this implacable wall of hostility from Republicans" to Obama's agenda over his nearly eight years in office.
Clinton has a comfortable delegate lead over rival Sen. Bernie Sanders in the race for the 2016 Democratic presidential nomination.