Trump repeatedly said debate moderator Megyn Kelly wouldn't treat him fairly and even polled his supporters asking if he should go despite her supposed bias.
After Fox mocked Trump's Twitter poll, Trump declared he wouldn't attend the Thursday-night debate.
Sen. Ted Cruz (R-Texas) was one of several presidential candidates to knock Trump for being "terrified" of Kelly.
"It's really quite astonishing that Donald is apparently so afraid of Megyn Kelly," Cruz said during a Fox News interview with Sean Hannity.
"If you're afraid of Megyn Kelly, then you're going to be afraid of Hillary Clinton. And you're going to be afraid of Vladimir Putin," he added, referring to the Russian president.
Cruz, Trump's top rival in the Iowa caucus next Monday, further said Trump's decision to skip the debate disrespected the voters there, who will be the first to weigh in on the Republican primary process. The Fox debate will also be in Iowa.
Trump said instead of attending the debate, he would host an event in Iowa on Thursday to benefit wounded veterans. Trump's campaign manager also said Wednesday that the debate decision wasn't about Kelly, but rather Fox's broader bias against his candidate.
But Cruz clearly didn't buy Trump's defense.
"This is a job interview. And if you want a job interview, the first thing you should do to get the job is show up at the interview," Cruz told Hannity. "And I think it's really remarkable that Donald Trump thinks so little of the men and women of Iowa that he is willing to skip the debate altogether. He doesn't think he should have any questions on his record."
Cruz's campaign also set up a website - DuckingDonald.com - further tweaking Trump for the debate boycott. The website declared that if Trump was so "afraid" of Kelly, the senator was willing to have a one-on-one debate with Trump anytime, anywhere.
Other campaigns bashed Trump with a similar line of attack.
Former Florida Gov. Jeb Bush (R) promoted a tweet from conservative radio host Erick Erickson asking how Trump would handle former Secretary of State Hillary Clinton, the Democratic front-runner, if he couldn't handle Kelly:
Exactly. https://t.co/kdZIrLCpwp
- Jeb Bush (@JebBush) January 27, 2016
If @megynkelly is too intimidating for Trump, how the hell is he gonna deal with Putin, etc? #loser
- John Weaver (@JWGOP) January 27, 2016
America wants a fighter who shows up. https://t.co/l64TB0ThPq @FoxNews #KellyFile
- Chris Christie (@ChrisChristie) January 27, 2016
"If somebody's treating you unfairly, it gives you an opportunity to expose that unfairness." @RealBenCarsonhttps://t.co/X1u6xi47iX
- FOX & Friends (@foxandfriends) January 27, 2016