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Sen. Ted Cruz (R-Texas).
Speaking on the Mark Levin Show, a conservative talk radio program, Cruz criticized the real estate mogul for his ongoing feud with Fox News host and debate moderator Megyn Kelly.
"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," Cruz said Tuesday night.
"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."
Cruz added that Trump could choose the moderator for the proposed debate, which he suggested in addition to Thursday's main debate in Des Moines.
Recent polls show Trump with a slight lead over Cruz in Iowa, with less than a week before the Hawkeye State's Feb. 1 caucus. Trump maintains a strong lead in national polls.
Earlier Tuesday evening, Trump confirmed his intention to skip the Fox News debate because of Kelly's supposedly biased coverage. Trump called Kelly "a third-rate reporter" and "a total lightweight" at a press conference in Marshallton, Iowa.
Cruz said Trump's reluctance to participate in Thursday's debate "speaks volumes."
"If he thinks Megyn Kelly is so scary, what exactly does he think he'd do with Vladimir Putin?" Cruz said. I promise you, Putin is a lot scarier than Megyn Kelly."