Donald Trump has called for a new Republican election in Iowa, accusing the winner, Ted Cruz, of fraud.

The billionaire pointed to the fact that during the caucus Ted Cruz’s campaign told voters rival Ben Carson planned to quit the race, which was not true.

The Cruz campaign apologized to Ben Carson, saying it was a misunderstanding.

Donald Trump came second in the first state-by-state contest to pick each party’s presidential nominee.

Next up is New Hampshire, where voters will make their choice in the Republican and Democratic races on February 9.

Donald Trump said: “Ted Cruz didn’t win Iowa, he stole it. That is why all of the polls were so wrong and why he got far more votes than anticipated. Bad!”

Earlier, he wrote on Twitter that Ted Cruz “illegally” won the caucus, but later deleted the tweet.

Paul Pate, the top election official in Iowa, condemned Ted Cruz campaign leaflets sent out prior to voting that accused Iowans of “voting violations”.

The leaflets graded Iowans and their neighbors for how much they had voted in the past and told them to turn out to improve their scores.

Paul Pate said Ted Cruz’s leaflets “misrepresent Iowa election law” and that they were “not in keeping in the spirit of the Iowa caucuses,” but he stopped short of any official action.

Donald Trump’s reaction contrasts with his concession speech on February 1, which was seen as a humble departure from his usual bombastic style.

He called second place “a long-shot great finish” in an earlier tweet.

Ted Cruz’s camp is not taking the accusations too seriously.

“Reality just hit the reality star – he lost Iowa and now nobody is talking about him, so he’s popping off on Twitter,” Ted Cruz’s communications director Rick Tyler told Politico in an email.

“There are support groups for Twitter addiction, perhaps he should find his local chapter.”

There is no precedent for re-staging a caucus.

Ben Carson accepted Ted Cruz’s apology about the drop-out rumors, but his campaign called the tactics “dirty tricks”.

The remaining candidates are now in New Hampshire, the next state to hold a primary vote, where Donald Trump is leading in the polls.

Also on February 3, Kentucky Senator Rand Paul and former Pennsylvania Senator Rick Santorum dropped out of the Republican race after disappointing finishes in Iowa.