Ben Carson is upset at Republican presidential rival Ted Cruz not because the latter bested him during Monday's Iowa caucuses but because he allegedly used "dirty tricks" to get ahead.

Carson accused Cruz's campaign staff of spreading rumours that he had already dropped out of the Republican race so that his voters would turn to Cruz.

"That is really quite a dirty trick," Carson told TIME. "That's the very kind of thing that irritated me enough to get into this quagmire."

Cruz later offered his apology to Carson, but the damage had already been done.

Carson's communications director Larry Ross said the "dirty tricks" employed by Cruz and his team are the very reason why Carson wanted to run for the presidency—to counter-attack the "Washington values of win at all cost."

Carson's campaign manager Ed Brookover is also fuming at Cruz's campaign tactic. "To have campaigns come out and send emails to their caucus speakers suggesting that Dr. Carson was doing anything but moving forward after tonight is the lowest of low in American politics," he said.

In his defence, Cruz said his campaign only acted accordingly when they saw a CNN news bulletin saying that Carson was no longer "carrying on to New Hampshire and South Carolina."

CNN, however, denied that it released such a news report.

"Our campaign updated grassroots leaders just as we would with any breaking news story," Cruz told CNN in a statement. "That's fair game. What the team then should have done was send around the follow-up statement from the Carson campaign clarifying that he was indeed staying in the race when that came out."

Moments later, Cruz apologised for the wrong information his camp helped spread. "This was a mistake from our end, and for that I apologise to Dr. Carson," he said.