Donald Trump today revealed the extraordinary memo a senior Ted Cruz operative sent to volunteers urging them to spread a false claim that Ben Carson had quit the White House race.

He tweeted a picture of a note sent by Spence Rogers, Cruz's deputy Iowa campaign director, just before the start of the Iowa caucuses on Monday night.

Trump called the actions by Cruz 'fraud' and believes it – and another election communication – may have cost him victory in Iowa.

He demanded a new election and threatened to sue – and was backed by Sarah Palin, who endorsed him before the caucus, who accused Cruz's campaign boss of 'lying'

Cruz himself today dismissed it as a 'Trumpertantrum' and accused the New Hampshire front-runner – who is trouncing Cruz 38-14 in the latest poll – of being less well-behaved than his young daughters.

Then he went on the offensive, CBS News reported, saying: 'I wake up every day and laugh at the latest thing Donald has tweeted, because he's losing it.

'But we need a commander-in-chief, not a Twitterer-in-chief. I don't know anyone who would be comfortable with someone who behaves this way having his finger on the button.

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Bombshell: Trump tweeted the letter Cruz's deputy campaign director in Iowa sent to urge volunteers to spread an untrue claim about Carson. Trump claims it cost him victory.

Fury: Trump, who campaigned in New Hampshire yesterday, turned on Cruz today demanding a fresh election

In the sights: Ted Cruz's campaign have already apologized for spreading false rumors about Ben Carson. But Carson held a press conference on 'deceptive Iowa caucus tactics'

Retort: Ted Cruz tweeted this message from the editor of the left-wing Thiink Progress

'We're likely to wake up one day and Donald, if he were president, would have nuked Denmark.'

He also tried to blame the media, ignoring the fact that it was Trump, Palin and Ben Carson – who held a press conference about 'deceptive Iowa caucus tactics – who launched the charge.

He had previously claimed that his staff had repeated a CNN report which implied Carson was to quit but tonight the network issued a strongly-worded statement refuting that claim.

'Senator Cruz's claims about CNN are false,' it said. 'At no point did the network indicate Dr. Carson would suspend his campaign.

'Our correspondent reported the information provided to him by the Carson campaign. Dr. Carson's staff informed CNN that he would return home to take a "deep breath" before resuming his activities on the trail.

'That information was reported accurately by CNN across TV and digital.'

Cruz also refused to sack the senior campaign worker who sent the message revealed by Trump.

Asked directly if the Cruz campaign was letting Rogers go, his press secretary Catherine Frazier responded that it was 'not true.'

'Iowa is over,' Frazier said Wednesday. 'But he’s still on the team, yes.'

She also noted that Cruz had told reporters today that 'he's not going to use staff as [a] scapegoat'.

Cruz made Trump, not his own errant staffer, the object of his anger, retweeting a message from a reporter at Think Progress, a left-wing blog, who wrote: 'Trump says he's upset at Ted Cruz for disrespecting Ben Carson. Which is kinda weird, considering Trump compared Carson to a child molester.'

Rogers has been a fixture in Cruz's Iowa campaign since early on.

The U.S. Army veteran's firm, Grow To Win Marketing, specializes in the kind of social media marketing services that political campaigns depend on to spread their messaging.

Cruz has made blaming the 'liberal' media a regular feature of his campaign, including a bad-tempered performance at the last Republican debate, but is now in the firing line of an increasingly angry Trump.

After tweeting the image from the Cruz campaign, he wrote: 'The State of Iowa should disqualify Ted Cruz from the most recent election on the basis that he cheated- a total fraud!'

Trump vs. Ted: The two candidates duked it out Wednesday on Twitter

In on the act: Marco Rubio piled on too, saying: 'You know, ultimately I think it goes back to what I said before, and that is [Cruz's] willingness to say or do anything – in this case, spread a false rumor about Ben Carson.'

Earlier Sarah Palin had used a lengthy Facebook post to attack Cruz and especially Steve King, a congressman who is Cruz's campaign chairman, who she accused of lying.

'He told voters Carson was dropping out of the Presidential race immediately before the Iowa caucus, causing a relative uproar inside the process, so the word would spread and he could rack up more votes for his candidate, Cruz. That's a dirty trick. Dr. Carson deserved better. The voters deserved better!' Palin wrote.

And Carson held a press conference in Washington DC on the issue, pointedly adding a scriptural reference to the notice inviting journalists to attend, saying: 'In Matthew 7, Jesus Himself says that a tree – and people of faith – are known by their fruit, not just the words they say.'

At the event he went on to say that Cruz had claimed directly to him that he had no idea about the false rumor being spread.

Carson appeared to cast some measure of doubt on that assurance as he said: 'He could have very well not known but it is obvious that there were people in his organization who carried it out.'

TED CRUZ, BEN CARSON, CNN AND AN EXPLOSIVE 'SMEAR' ROW Ted Cruz put his name to a statement on Tuesday apologizing to Carson which said: 'Last night when our political team saw the CNN post saying that Dr. Carson was not carrying on to New Hampshire and South Carolina, our campaign updated grassroots leaders just as we would with any breaking news story. '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.' CNN hit back on Wednesday saying: 'Senator Cruz's claims about CNN are false. At no point did the network indicate Dr. Carson would suspend his campaign. 'Our correspondent reported the information provided to him by the Carson campaign. Dr. Carson's staff informed CNN that he would return home to take a "deep breath" before resuming his activities on the trail. 'That information was reported accurately by CNN across TV and digital.' And here's what CNN reported originally in tweets from Chris Moody, senior reporter for CNN politics: 'Ben Carson will likely speak at his victory party in Iowa before caucus results are in so he can catch a flight. 'Carson won't go to NH/SC, but instead will head home to Florida for some R&R. He'll be in DC Thursday for the National Prayer Breakfast.' Advertisement

That's a direct tweak at Cruz, who has cited the same Bible verse at dozens of campaign events, using it to suggest that some 'fake' conservatives – usually a reference to Trump and Marco Rubio – can't withstand the scrutiny of being judged by their liberal or centrist pasts.

Carson's attack is the first time Cruz has been attacked on his Christian credentials after months carefully courting evangelicals.

Rubio himself leaped into the anti-Cruz free-for all on Wednesday in New Hampshire, trying to gain ground on his fellow senator and overtake him for second place in polling.

Asked if Trump was right in claiming Cruz 'stole' his Iowa caucus victory, Rubio said: 'I don't know exactly what he means by that.'

But moments later he made it clear that he caught the questioner's drift. 'Obviously we've all seen the reports of the rumors they spread about Ben Carson, and you know those weren't accurate and I thought it was unfair to Ben,' he said.

'You know, ultimately I think it goes back to what I said before, and that is [Cruz's] willingness to say or do anything – in this case, spread a false rumor about Ben Carson.'

It is Trump, however, who is leading the charge.

He is hoping to bounce back with victory in New Hampshire where a 7News/UMass Lowell tracking poll published on Wednesday morning showed him ahead of Cruz by 38% to 14%.

He also highlighted a letter sent from the Cruz campaign which appeared to warn voters they were in 'violation' of electoral law if they did not attend the caucuses.

The extraordinary series of Tweets came after Cruz beat the billionaire into second place in the Iowa caucus - a result which defied some polls.

But Cruz did apologize for his campaign's emails to supporters claiming that Carson was withdrawing from the race - which meant that Carson's caucus-goers would instead support Cruz. Cruz called it 'a mistake.'

Trump stepped up his attack Wednesday afternoon with two tweets calling Cruz to task for his campaign's tactics.

'The State of Iowa should disqualify Ted Cruz from the most recent election on the basis that he cheated- a total fraud!'

Another tweet re-posted a screen-shot of the email that Cruz's campaign sent out.

The Twitter war continued with a fire-back from Cruz.

'Yet another #Trumpertantrum... @realDonaldTrump very angry w/the people of Iowa. They actually looked at his record,' Cruz's campaign tweeted.

Back-up: Sarah Palin's lengthy attack on Cruz came after Trump's Tweets

How Trump revealed the Ted Cruz official communication. He also revealed a tweet from a Cruz supporter (bottom right) which claimed that Carson sources had confirmed he was out - which was untrue

And another:

How a person conducts his life or campaign is an indication of who he is. In Matthew 7, Jesus Himself says that a tree - and people of faith - are known by their fruit, not just the words they say Notice announcing Ben Carson's press conference, reported by PBS. Cruz quotes the verse frequently himself in stump speeches

Trump later threatened to sue when he appeared on a Boston radio station.

Speaking on Boston Herald Radio, Buzzfeed reported that he was asked if he would sue and said: 'I probably will; what he did was unthinkable.

'He said "the man has left the race" and he said it during the caucus.'

In his apology, Cruz blamed the error on his 'team' and claimed they were simply repeating CNN - a point refuted explicitly by CNN tonight.

'Last night when our political team saw the CNN post saying that Dr. Carson was not carrying on to New Hampshire and South Carolina, our campaign updated grassroots leaders just as we would with any breaking news story,' Cruz said 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.'

Carson called it 'really quite a dirty trick,' but later said he accepted the apology.

He also called for the firing of Cruz's campaign staffer who sent out the tweet.

'I think whoever is responsible for blatant lying should be dismissed, absolutely. Unless that kind of behavior is acceptable in your campaign culture,' Carson told CNN.

But Cruz's campaign also got into trouble for a different reason over the weekend.

The campaign sent out an email to his supporters that was intended to look official - but wasn't - that warned would-be caucus-goers about 'low voter turnout in your area.'

The email even included the recipient's voting history as well as their neighbors and was marked: 'VOTING VIOLATION' and said 'official public record'.

A campaign staffer for Ted Cruz sent out this letter on Saturday - which was taken to be an official legal communication to scare people into voting

'Your individual voting history as well as your neighbors' are public record,' the email said.

'Their scores are published below, and many of them will see your score as well. CAUCUS ON MONDAY TO IMPROVE YOUR SCORE and please encourage your neighbors to caucus as well.'

'A follow up notice may be issued following Monday's caucuses.'

Iowa Secretary of State Paul Pate issued a statement disavowing the email and saying that it 'misrepresents Iowa election law.'

Cruz's retweet of a claim that Trump likened Carson to a child molester was one of the day's odder developments.

That was a reference to a November CNN interview in which the billionaire commented Carson's autobiographical description of his own anger issues as a teen.

'It's in the book that he's got a pathological temper,' Trump told anchor Erin Burnett then.

'That's a big problem because you don't cure that ... as an example: child molesting. You don't cure these people. You don't cure a child molester. There's no cure for it. Pathological, there's no cure for that.'

Trump said on Good Morning America that he wasn't 'thrilled' that he lost to Ted Cruz on Monday night

'I don't like second place. I'm not a fan of second place, but I did well,' Trump said this morning. 'But I was told don't even go to Iowa, because I'm not going to win Iowa. And I thought it was something I should do and I went there and I almost won it.'

Today Trump said on Morning Joe he was not suggesting his presidential bid had been a waste of time or that he might eventually quit.

Rather, he was saying he'd spent his own savings on his campaign and would have been better off accepting the checks he rejected from his rich friends.

'I don't mind taking in two, three, hundred million dollars,' he said.

Trump again said he doesn't gets 'any credit for self funding' and said, 'In other words the voters aren't going into the booth saying, 'Oh, Trump is self funding his campaign, that's a big factor and therefore I'm going to vote for him.' '

WIDE MARGIN: Donald Trump may have finished second in Iowa but he's crushing the Republican field in New Hampshire according to the latest statewide poll

Morning Joe host Joe Scarborough asked if that meant Trump would change course and being taking money from outside actors.

'No,' Trump replied. 'I said I wasn't going to change.'

He added: 'I just don't think it's fair. I'm the only one not taking money from the lobbyists and the special interests.'

MSNBC proceeded to show a chart sourced to the Washington Post that determined Trump spent $300 per vote in Iowa, while Rubio spent a $600 and Cruz dished out $700 per person.

It also had Rand Paul at $1,500, Ben Carson at $3,100 and Jeb Bush at $5,200.

'If I am investing in Donald Trump's operation, I would invest with a guy that gets the most bang for his buck, that is you,' Scarborough told him.

'But then there's a question, should you have spent more money in Iowa?' he said. 'Will you spend more money to make sure you finish the deal in future states?'

Trump said 'there's no limit on the spending' implying that he could direct more of his personal resources to his presidential campaign.

And he reiterated that his Iowa loss wasn't as important as the media is making of it. 'Everyone told me I couldn't win so I sort of just went through the motions a little bit,' he claimed.

He was mocking the Texas senator's 32-minute address, comparing it to the shriek the Democratic candidate bellowed out in 2004, which punctuated the end of his campaign.

Cruz, who was polling below Trump in the days leading up to the caucuses, had a decisive victory in the Hawkeye state.

He received 27.65 percent of the vote, compared to Trump's 24.31 percent. Rubio, in third place, received 23.1 percent.

Cruz bested Trump by more than 6,000 votes.