Cruz did not answer the question, but instead launched into an explanation of how he thinks the immigration system should be changed, starting with finding areas of bipartisan agreement such as securing the border, and then streamlining legal immigration.
"But that doesn't sound like an answer," Kelly said. "Mr. Trump answered that question explicitly last night on 'The O'Reilly Factor.' Will you do so now?"
Cruz would not and instead discussed how he thinks Congress should fix the immigration system.
"You've outlined your plan, but . . . you're dodging my question. You don't want to answer that question?" Kelly asked.
No, said Cruz, who both smiled and sounded irritated at points, adding: "But Megyn, I'm not playing that game."
Trump -- whose immigration plan Cruz has said falls into step with his own -- said that he would deport the children. Cruz would not say how he would handle the situation.
"Megyn, I get that's the question you want to ask. That's also the question every mainstream media liberal journalist wants to ask," Cruz said.
"Is it unfair?" Kelly asked.
"It's a distraction from how we actually solve the problem. You know it's also the question Barack Obama wants to focus on," Cruz said.
"But why is it so hard?" Kelly asked. "Why don't you just say yes or no?"
Cruz did not say yes or no. Instead he pivoted back to the idea that "we need to solve the problem" of illegal immigration. "Once we solve that problem, then we can have a debate. Then we can have a conversation."
Trump attacked Kelly after she aggressively questioned him during this month's Republican presidential debate over his history of offensive statements about women.
"She gets out and she starts asking me all sorts of ridiculous questions," Trump said in a CNN interview earlier this month. "You could see there was blood coming out of her eyes, blood coming out of her wherever. In my opinion, she was off base."
Trump again attacked Kelly on Twitter Monday and Tuesday, including saying she was "off her game" after coming back from vacation.
Fox News Chairman and CEO Roger Ailes issued a statement Tuesday calling Trump's most recent attacks on Kelly "bullying" and said it is "as unacceptable as it is disturbing."
Ted Cruz exits the presidential race
Correction: An earlier version of this post had the word "liberal" missing from the following quote: "That's also the question every mainstream media liberal journalist wants to ask." The quote has been amended.