But the senator from Texas refused to join other 2016 Republican hopefuls in denouncing the real estate mogul.
Trump sparked an uproar when he suggested at the Family Leadership Summit in Ames, Iowa, that McCain wasn't a war hero because he was captured. "He is not a war hero," Trump said at a question-and-answer session. "He is a war hero because he was captured. I like people that weren't captured, OK? I hate to tell you. He is a war hero because he was captured. OK, you can have -- I believe perhaps he is a war hero."
He later tried to clean up his comments, but a wave of Republicans had already condemned Trump's remarks.
For his part, Cruz told reporters he considers McCain "a friend" whom he respects and admires.
"Not only did he sign up to defend our nation, putting his life in harm's way, but when he was a POW, he was imprisoned, tortured, and most incredibly, he was offered the opportunity for early release, he was offered the opportunity to go home, and he turned it down because he believed it would be dishonorable to accept that."
But he declined to speak ill of his presidential rival, with whom he met earlier this week in New York
after becoming the most notable 2016 hopeful to side with Trump
over his controversial remarks on immigration. Instead, Cruz on Saturday blamed the media for trying to pit Republicans against each other.
"You know I recognize that folks in the press love to see Republican-on-Republican violence, and so you want me to say something bad about Donald Trump, or bad about John McCain or bad about anyone else," he said. "I'm not going to do it."
Retired neurosurgeon Ben Carson suggested that Trump's comments were stupid, but was also hesitant to wade into the debate. Asked by reporters whether he considered McCain a war hero, Carson said, "It depends on your definition of a war hero."
"I think he has done some wonderful things, certainly history is consistent with what we would consider a war hero," he added. "Do we take that away from him because some people disagree with him politically? I think that's probably stupid."
Asked again if, in his view, McCain was a war hero, Carson simply said, "I believe Senator McCain has done some wonderful things."