Donald Trump and Ted Cruz. REUTERS/Jonathan Ernst A spokesman for Sen. Ted Cruz (R-Texas) has shot back at Donald Trump after the real-estate mogul accused Cruz of stealing a win in the Monday-night Iowa caucuses.

In a string of tweets Wednesday morning, Trump accused Cruz of "illegally" stealing the victory and suggested that Cruz's vote total should be "nullified." He later went on Boston Herald Radio and said that he would "probably" file a formal complaint over the caucus results.

Rick Tyler, a spokesman for the Cruz campaign, then suggested in a statement to NBC News that Trump should check in to a "Twitter addiction therapy group."

"Reality has hit the reality star," Tyler said. "Since Iowa, no one is talking about Donald Trump. That's why he's popping off on Twitter. There are Twitter addiction therapy groups, and he should check in with his local chapter."

Cruz's official account also tweeted about the feud, taking a swipe at Trump's past of favoring more liberal-leaning policies, especially on healthcare:

Bernie is contesting #IA results. Maybe Donald should go back to IA & join the Ds. Bet they'd love #TrumpCare https://t.co/uTdU9Uv9sL — Ted Cruz (@tedcruz) February 3, 2016

Trump's claims of fraud center on the actions of Cruz allies caucus night.

A third Republican candidate, Ben Carson, had reportedly signaled that he was going to speak early that night in order to fly home to Florida and rest. This was a somewhat unusual declaration as most candidates were planning to rush to the next primary states.

Some Cruz supporters quickly speculated that Carson was about to leave the race. Rep. Steve King (R-Iowa), a prominent Cruz surrogate, wrote on Twitter: "Carson looks like he is out. Iowans need to know before they vote. Most will go to Cruz, I hope."

Cruz later apologized to Carson and said his team should have circulated Carson's statement denying the rumors.

The Texas senator ultimately won the caucuses despite the fact that Trump had been leading polls for weeks before the voting started.