Fox News
"Of course not," Cruz told Fox News' Megyn Kelly on Tuesday.
Cruz said because the evidence used to justify the war - that Iraq was in possession of weapons of mass destruction - turned out to be false, there was "no way we would have gone to war with Iraq" in hindsight.
Bush and Cruz are likely rivals in the 2016 presidential race.
"The entire predicate of the war against Iraq was the intelligence that showed they had weapons of mass destruction and that there was a real risk that they might use them," Cruz said. "Now I would note there was a bipartisan consensus of both Republicans and Democrats looking at that intelligence [who] concluded it was a real threat. We now know that intelligence was false."
Cruz's response contrasts sharply with what Bush told Kelly in an interview that aired Sunday. Kelly asked Bush to look back with the information the US has today, but Bush appeared to misinterpret her question and said he would have supported the war at the time.
"I would have [authorized the invasion], and so would have Hillary Clinton, just to remind everybody. And so would have almost everybody that was confronted with the intelligence they got. In retrospect, the intelligence that everybody saw, that the world saw, not just the United States, was faulty," Bush said.
The question is potentially an awkward one for Bush because his brother, former President George W. Bush, led the invasion that became widely unpopular after no WMD's were found. Indeed, pressed again on Tuesday, Bush did not offer a clear answer on whether the US should have gone to war. Bush only said he would have made a different decision, declining to speculate on the hypothetical.
"I interpreted the question wrong, I guess," he told conservative radio host Sean Hannity, according to audio posted by Mediaite. "I don't know what that decision would have been; that's a hypothetical. But the simple fact is mistakes were made. As they always are in life."
Another likely presidential contender, New Jersey Gov. Chris Christie (R), also gave a clear answer on the invasion of Iraq on Tuesday.
"I want to directly answer your question because that's what I do," Christie said on CNN. "If we knew then what we knew now, and if I were president of the United States, we wouldn't have gone to war. But we don't get to replay history."
Watch Cruz's interview on Fox News below: