“We’ve had five great debates in this campaign. Unfortunately, Donald Trump has ducked all of them,” Ms Haley said in a statement on Tuesday. “He has nowhere left to hide. The next debate I do will either be with Donald Trump or with Joe Biden. I look forward to it.”
Still, following the caucuses, Ms Haley said, “I can safely say tonight Iowa made this Republican primary a two-person race.”
Last week, Ms Haley went head-to-head in a debate with Mr DeSantis. Their ratings on CNN were trounced by Mr Trump’s appearance at the same time on a Fox News town hall.
Other debates are scheduled for 18 January and 21 January ahead of the first-in-the-nation primary held in New Hampshire.
Mr DeSantis wrote on X that he believes Ms Haley “is afraid to debate because she doesn’t want to answer the tough questions such as how she got rich off Boeing after giving them millions in taxpayer handouts as governor of South Carolina.”
He added, “The reality is that she is not running for the nomination, she’s running to be Trump’s VP.”
He said unlike Mr Trump or Ms Haley, “I won’t snub New Hampshire voters” and “plan to honour my commitments”.