Opening up an onslaught on Cruz, runner-up Donald Trump described him as a liar and accused him of fraud by "stealing" votes.
Cruz, who appears more confident after his Monday victory in the crucial Caucus and has support of conservatives, fought back by saying that this was another "tantrum" of Trump.
The war of words continued yesterday not only at public meetings, but also in the social media, particularly Twitter.
"Yet another Trumpertantrum," Cruz fought back, adding that Trump is very angry with the people of Iowa. "They actually looked at his record."
"I wake up every day and laugh at the latest thing Donald has tweeted. Because he's losing it. We need a commander in chief, not a twitterer in chief," he said after Trump went on the social media to lash out at the Texas Senator.
"I think, what he (Cruz) did was disgusting," Trump told a news channel.
Such allegations are rare in US electoral politics.
A similar war of words was also witnessed in the rival Democratic camp as Hillary Clinton and Bernie Sanders traded barbs over who best embodies progressive values ahead of the New Hampshire primary next Tuesday.
Vermont Senator Sanders alleged that Clinton is out of step with the party's base on issues ranging from campaign finance to climate change, trade and the Iraq War.
Clinton shot back, saying she was "amused" that Sanders appears to consider himself the "gatekeeper on who's progressive".
"I do not know any progressive who has a super-PAC and takes USD 15 million from Wall Street. That's just not progressive," Sanders said during a CNN town hall.
"Secretary Clinton has been a supporter in the past of
various trade policies with China. Reluctantly, and after a lot of pressure on her, she came out against the TPP (Trans- Pacific Partnership), and I'm glad that she did," Sanders said.
"Every sensible person understands that climate change is real. It is caused by human activity. And we have got to transform our energy system away from fossil fuel.
Clinton fought back soon thereafter.
"I was somewhat amused today that Senator Sanders has set himself up to be the gatekeeper on who is the progressive because under the definition that was flying around on Twitter and statements by the campaign, Barack Obama would not be a progressive, Joe Biden would not be a progressive, Jeanne Shaheen would not be a progressive, even the late, great Senator Paul Wellstone would not be a progressive," she said.
