Republicans Donald Trump and Sen. Ted Cruz on the CNN debate stage. (AP File Photo)

(CNSNews.com) - After Donald Trump announced that he will not take part in the Fox News debate scheduled for Thursday night in Des Moines, Iowa, Sen. Ted Cruz (R-Texas) challenged Trump to go one-on-one with him, with or without moderators:

Appearing on Mark Levin's radio show Tuesday night, Cruz said, "If Donald is afraid of Megyn Kelly, I would like to invite him, on your show, to participate in a one-on-one debate, between me and Donald, mano a mano.

“Now we could do it a number of ways. We could have you moderate it, Mark. We could have Sean Hannity moderate it. We could have Rush Limbaugh moderate it.

“But you know what, if he's afraid of Megyn Kelly, if he's afraid of you, and afraid of Hannity and afraid of Rush -- then we could do it without any moderators whatsoever.

“I'm happy to go an hour and a half, mano a mano, me and Donald, with no moderators, any time before the Iowa Caucuses. That's what a candidate who actually wants to work for the people, wants to -- to earn the support of the people will do, is you stand up and defend your record.

“And so I would invite Donald, let's do this...

"And by the way, he's been saying this past week that he thinks I'm stupid. Then he should do very well in a debate with someone who's so stupid, away from moderators that he is so afraid of.”

Cruz, now on a bus tour across Iowa, said Iowa is a close, two-man race. He said every presidential candidate "owes it to the voters" to answer their hard questions.

He said the fact that Trump "is now afraid to appear on the debate stage" to have his record questioned shows "a lack of respect for the men and women of Iowa."

"We've had seven years of a narcissistic president, who has a messiah complex," Cruz said. "No individual candidate -- it's not about Donald, it's not about me, it's about the American people.

"If anyone wants to be president, you need to demonstrate the humility -- 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. 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.



“And I'd like to hear Donald explain to the American people, the people of Iowa, how he is prepared to be commander in chief, if he's terrified by a television host."

Speaking in Iowa City on Tuesday, Trump said he wouldn't allow the Fox network to "toy" with him. He has demanded the removal of Kelly as a moderator in Thursday’s debate, but Fox refused his request.

"I'm not a fan of Megyn Kelly. I think she's a third-rate reporter," Trump said on Tuesday. "I think she frankly is not good at what she does. And I think they could do a lot better than Megyn Kelly. And so I'm going to be making a decision with Fox, but I probably won't bother doing the debate."

Trump said he'll be doing something else Thursday night in Iowa: "We'll do something where we raise money for the veterans and the Wounded Warriors. We're going to do something simultaneously with the debate. But most likely I'm not going to do the debate."

Trump's spokesman later said Trump definitely would not take part in the Fox debate.

On the campaign trail Tuesday night, Trump objected to a "wise-guy" press release issued by Fox on Tuesday:

"And then when I see a press release written by a child like I just saw, I said..Why do I have to make Fox rich? Let me make the Wounded Warriors rich, let me make the veterans rich."

The Fox statement read: "We learned from a secret back channel that the Ayatollah and Putin both intend to treat Donald Trump unfairly when they meet with him if he becomes president — a nefarious source tells us that Trump has his own secret plan to replace the Cabinet with his Twitter followers to see if he should even go to those meetings."

"The debate will go on, with or without Mr. Trump," Megyn Kelly said Tuesday night.

For the record, this is the question that Kelly asked Trump in the debate last August, earning Trump’s enduring resentment: