Trump mocks Cruz debate challenge: 'Can we do it in Canada?'
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Republican presidential front-runner Donald TrumpDonald John TrumpIvanka Trump pens op-ed on kindergartners learning tech Bharara, Yates tamp down expectations Mueller will bring criminal charges Overnight Cybersecurity: Equifax security employee left after breach | Lawmakers float bill to reform warrantless surveillance | Intel leaders keeping collusion probe open MORE on Wednesday lashed out at rival Ted CruzRafael (Ted) Edward CruzWhatever you think the Alabama special election means, you’re probably wrong This week: Congress gets ball rolling on tax reform Week ahead: Senators work toward deal to fix ObamaCare markets MORE for challenging him to a one-on-one debate.

"Even though I beat him in the first six debates, especially the last one, Ted Cruz wants to debate me again," Trump tweeted on Wednesday. "Can we do it in Canada?"

Trump has repeatedly attacked Cruz for being born in Canada, suggesting it makes him unqualified to be president. Trump has also referred to him as "the Canadian."

Cruz on Tuesday night challenged Trump to a one-on-one debate, hours after Trump said he would not participate in Thursday's GOP debate on Fox News.

“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 y mano,” Cruz said during an interview on “The Mark Levin Show,” adding that Trump could choose the moderator.

Trump had said he would not participate in a Fox debate that Kelly moderated because he does not believe she could treat him fairly. Trump on Tuesday called Kelly a "lightweight" and "not a reporter."

The two rivals have been ratcheting up their attacks on each other with polls showing that they're neck-and-neck for first place in Iowa less than a week out from the state's caucuses.

Trump has repeatedly brought up Cruz's Canadian birthplace and his reputation of being divisive during his time in the Senate, calling him a "nasty guy" that "nobody likes."

Cruz meanwhile, has criticized his rival for his "New York values" and for being willing to negotiate with Democrats.

"So if, as a voter, you think what we need is more Republicans in Washington to cut a deal with Harry Reid and Nancy Pelosi and Chuck Schumer, then I guess Donald Trump's your guy," Cruz said during an interview on MSNBC last week.

--This report was updated at 3:13 p.m.