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

Trump pointed to the fact that during the caucus the Cruz campaign told voters rival Ben Carson planned to quit the race, which was not true.

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

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 Tuesday.

"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!" Mr Trump said.

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

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

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

Pate said 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.

The reaction contrasts with his concession speech on Monday night, which was seen as a humble departure from his usual bombastic style.

Trump called second place "a long-shot great finish" in an earlier tweet.

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," 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.

Carson accepted Cruz's apology about the drop-out rumours, 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 Trump is leading in the polls.

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

(BBC)