Story highlights Ted Cruz for a third time would not say that he would support Donald Trump as the GOP nominee

Cruz is inviting Trump to appear together with him Tuesday at CNN's town hall

Washington (CNN) Ted Cruz for a third time would not say that he would support Donald Trump as the GOP presidential nominee, the latest sign that his pledge to do so may be softening.

Cruz late last week began signaling that his unconditional support for the Republican front-runner was not as ironclad as previously. But asked by CNN's Sunlen Serfaty on Monday if he would definitively say that he would not support Trump, the Texas senator left his answer ambiguous.

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"I'm not in the habit of supporting people who attack my wife and attack my family," Cruz said. "Donald Trump is not gonna be the nominee. We are gonna beat him for this nomination."

Pressed why he would not come out and say that Trump wouldn't have his support in a general election -- which some of his female supporters have said -- Cruz continued to evade a direct answer.

"What I am saying is we are going to beat Donald Trump for the nomination. We are seeing Republicans uniting," he said. "The best way to prevent Donald Trump from being the nominee is beat him at the ballot box, and that's what we are doing right now."