Republican presidential candidates Donald Trump (left) and U.S. Sen. Ted Cruz, R-Texas, speak during a commercial break in a Republican presidential debate Jan. 14, 2016, in North Charleston, South Carolina. Scott Olson/Getty Images

UPDATE 10:55 p.m. EST: Republican candidate Carly Fiorina tweeted that her campaign will donate millions of dollars to veterans' causes if Donald Trump will participate in a debate against her Thursday night. She also offered another donation to veterans' causes to be included in a potential debate between Ted Cruz and Trump Saturday night.

Original Story:

After Republican presidential candidate Donald Trump announced his decision to bow out of Thursday night’s GOP debate, rival candidate Ted Cruz challenged the billionaire businessman to a one-on-one debate. In response to the offer, Trump's campaign told ABC News, "If he's the last man standing and it comes down to a two-person race, Donald Trump will be happy to debate him."

In a letter to Trump, the U.S. senator from Texas invited the businessman to take part in a two-hour town hall-style event at Western Iowa Tech Community College in Sioux City, Iowa, at 8 p.m. CST Saturday.

“We owe it to the men and women if Iowa to ensure that they hear jointly and directly from the two leading Republican candidates so that they may contrast our positions on the critical issues we face as a nation as they make their final choice leading up to Monday’s caucuses,” Cruz said in a letter to Trump, a CNN journalist tweeted.

In the letter, Cruz suggested that the debate could be moderated by conservative commentators such as like Mark Levin, Sean Hannity, Glenn Beck or Rush Limbaugh. Cruz even launched a website titled that asks supporters to check “yes” to a debate between himself and Trump, ABC News reported.

Earlier this week, the real estate mogul announced that he would boycott Thursday night’s debate after Fox News refused to replace its anchor, Megyn Kelly, as a moderator. Kelly and Trump had clashed at the first Republican debate in August.

“Megyn Kelly’s really biased against me,” Trump said in an Instagram video posted Tuesday. “She knows that. I know that. Everybody knows that. Do you really think that she can be fair at a debate?”