Republican presidential candidate Ted Cruz Rafael (Ted) Edward CruzSenate Republicans face tough decision on replacing Ginsburg Cruz: Trump should nominate a Supreme Court justice next week Renewed focus on Trump's Supreme Court list after Ginsburg's death MORE tried to paint himself as the candidate for women on Wednesday, drawing a contrast with Donald Trump Donald John TrumpObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE, the GOP front-runner whose campaign has been marked by notable skirmishes with women.

The Texas senator rolled out a “Women for Cruz” coalition with his wife, his mother and former GOP hopeful Carly Fiorina. Cruz was the only man on stage for the launch of the coalition, which his campaign website says consists of more than 23,000 members.

Before a mostly male audience in Madison, Wis., Cruz made a pitch to female voters and provided insight into his relationships with the women in his life.

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“This event this morning is a celebration of strong women,” Cruz said. “The purpose of this event this morning is to take some time to introduce three strong women that I admire, who I respect, who I’ve learned from, who exemplify the incredible opportunity that America presents to everyone.”

Cruz delivered a sharp rebuke against Democrats for "pigeonholing" women and criticized the party for establishing certain issues as important to women.

“One of the most frustrating things about the Democratic Party is that Democrats love to pigeonhole women,” Cruz said. “You have a set of issues that are women’s issues.

“Women are not a special interest. Women are a majority of the United States of America, and every issue is a women’s issue,” Cruz continued.

The event comes amid Cruz and Trump’s ongoing feud involving their spouses.

Trump tweeted a picture last week comparing Heidi Cruz and his wife, in what he said was a response to an anti-Trump super-PAC ad featuring Melania Trump posing nude in 2000 for British GQ.

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The Texas senator has repeatedly denied any connection to the super-PAC and has pushed back at the GOP front-runner, saying “real men don’t attack women.”

The fight came up at Tueday’s CNN town hall, when Trump was asked about it by moderator Anderson Cooper. Cooper told Trump he had the argument of a 5-year-old when the candidate tried to defend his reposting of the image comparing the women.

At the Wednesday event, Heidi Cruz touted her husband's commitment to female voters nationwide. She didn't address the current feud between her husband and Trump.

"I want all of the women here in Wisconsin and across this country, to know how incredibly supportive ... he has always been of all the women in his life," she said. "I want you to know as voters he'll be equally supportive of you and your families."

The event comes one day after Trump’s campaign manager, Corey Lewandowski, was charged with battery for allegedly grabbing former Breitbart reporter Michelle Fields.

Following the charges, the GOP front-runner fiercely defended Lewandowski and questioned the legitimacy of a picture Fields tweeted showing bruises on her arm.

Cruz and Trump are in a tight race in the Badger State, which holds its primary on April 5. Cruz leads the GOP front-runner by less than 1 point, according to RealClearPolitics.

The Texas senator got a significant endorsement on Tuesday from Wisconsin Gov. Scott Walker, who called Cruz "a principled constitutional conservative who can win."