By Steve Holland and John Whitesides
Trump boycotted the debate in a snub to host Fox News, holding a competing event across town in Des Moines in a controversy that widened the rupture between his supporters and the Republican Party establishment.
"I'm a maniac and everyone on this stage is stupid, fat and ugly, and Ben, you're a terrible surgeon," Cruz said to rival Ben Carson, a retired neurosurgeon, saying that he had now "gotten the Donald Trump portion of the program out of the way."
"I want to thank everyone here for showing the men and women of Iowa the respect to show up and make the case to the people of this state and the people of the country why each of us believe we would make the best commander in chief," said Cruz, the Texas senator who is Trump's top rival in Iowa.
The billionaire front-runner for the Republican nomination for the Nov. 8 election withdrew from the encounter in a spat with network anchor Megyn Kelly whom he accuses of treating him unfairly.
"The 'debate' tonight will be a total disaster," Trump said in a Twitter post on Thursday morning. "Low ratings with advertisers and advertising rates dropping like a rock. I hate to see this."
A Fox News spokesperson rejected Trump's statement, saying: "The debate is completely sold out. No rates have changed and there are no advertisers who have backed out."
Cruz and other rivals had mocked Trump for skipping the debate since his decision on Tuesday. Cruz called him a "fragile soul" and offered to debate him one-on-one.
Trump's move might be a risky gamble ahead of Monday's Iowa caucuses, which kick off the state-by-state race to pick the nominees in the Nov. 8 presidential election.
But his support in the polls, much of it from blue-collar men, has not wavered for months despite him insulting Mexican immigrants, threatening to deny Muslims entry to the United States and fighting with Republican establishment figures like Senator John McCain.
Trump won backing on Thursday when two Republican candidates, Rick Santorum and Mike Huckabee, agreed to attend his alternative event, a fundraiser for veterans at Iowa's Drake University, during the Fox News debate.
The pair, social conservatives who have long been at odds with the more mainstream Republican establishment, had been relegated to the Fox News "undercard" debate of the candidates with low polling taking place earlier than the full-blown debate.
"The people of Iowa, who I know pretty darn well, care a lot about the issues," Santorum said, adding they wanted to hear a discussion of national security and other topics.
"And we are not hearing any of those things. We are hearing about whether someone is going to show up for the next debate or not," he said in the early debate, which also featured former Virginia Governor Jim Gilmore and former business executive Carly Fiorina.
A CNN source said the network would likely air parts of the Trump event live.
Trump announced a dedicated website, DonaldTrumpForVets.com, for his supporters to donate funds for military veterans.
"It is my great honor to support our Veterans with you!" Trump tweeted. The website, however, did not specify any particular charity to which the funds would go. (Additional reporting by Ginger Gibson and James Oliphant in Iowa, Doina Chiacu and Valerie Volcovici in Washington, Richard Valdmanis in Boston and Emily Flitter in New York; Editing by Alistair Bell and Peter Cooney)