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"And the fact that Donald is now afraid to appear on the debate stage, that he doesn’t want his record questioned, I think that reflects a lack of respect for the men and women of Iowa, that he’s unwilling to go to Des Moines and be questioned."

Cruz also argued that Trump dropping out of the debate shows that the front-runner isn't qualified to be president.

“This is a job interview, you need to be willing to answer the questions of the American people, and if Donald is afraid to defend his record, that speaks volumes,” he said.

“And if he thinks Megyn Kelly is so scary, what exactly does he think he’d do with Vladimir Putin? I promise you Putin is a lot scarier than Megyn Kelly."

Cruz added that Trump needs to explain to voters “how he is prepared to be commander-in-chief if he’s terrified of a television host.”

The comments came shortly after the Trump campaign announced Tuesday that he would not participate in the Fox News debate on Thursday.

In a press conference on Tuesday, Trump referred to Kelly as "lightweight" and said that she's "not a reporter."

- Updated at 8:45 p.m.