Donald Trump has accused Ted Cruz of fraud in the Iowa caucuses and Rand Paul has dropped out of the crowded Republican race to become the party's US presidential candidate.

In attacks posted on his official Twitter account, Mr Trump said "either a new election should take place or Cruz results nullified" in Monday's Iowa contest. The billionaire businessman placed second behind the conservative Texas senator.

A previous tweet from Mr Trump accused the Cruz campaign of telling Iowa voters that Ben Carson was quitting the race so he could steal Mr Carson's votes.

Meanwhile, Mr Paul said he will now turn his full attention to his Senate re-election campaign in Kentucky. He never caught on with voters beyond the small group of libertarian-leaning Republicans who backed the previous White House bids of his father, Ron Paul.

Florida Senator Marco Rubio, who placed third among the Republicans in Iowa, said he will try to persuade some of Mr Paul's supporters to redirect their support to him, despite the stark differences the two have on foreign policy.

Both men were elected to the Senate during the rise of the conservative tea party in 2010. Mr Rubio is trying to be the Republican establishment's preferred alternative to Mr Trump or Mr Cruz.

For the Democrats, Hillary Clinton was seeking to turn a narrow victory in Iowa over Vermont Senator Bernie Sanders into some momentum for her shaken Democratic campaign.

The former secretary of state and first lady defeated Mr Sanders by less than three-tenths of 1%, the closest result in Iowa Democratic caucus history, the state party said.

New Hampshire is the second in a series of state-by-state nominating contests to decide who will be each party's candidate for president in November.

Polls show Mr Sanders leading by double digits in New Hampshire, which neighbours Vermont.

Mr Trump has been leading the Republican polls in New Hampshire, which has historically favoured more moderate candidates than Iowa.

Polls show well over half of Republican voters have yet to make up their minds. Ohio Governor John Kasich, former Florida Governor Jeb Bush and New Jersey Governor Chris Christie all hope New Hampshire will breathe life into their flagging campaigns.

Candidates are also looking ahead to the more diverse South Carolina, which holds the first primary in the South later this month.