Official results more than two hours after polls closed showed the former UN ambassador had just 32 per cent of the vote, against more than 61 per cent for “None of these candidates”.

Trump’s team had encouraged his supporters to vote against his sole rival for the party nomination, even as he sat out the ballot.

US media, including NBC and ABC, projected the result would not change.

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Haley’s campaign brushed off the result.

“Even Donald Trump knows that when you play penny slots the house wins. We didn’t bother to play a game rigged for Trump. We’re full steam ahead in South Carolina and beyond,” a spokesperson told CNN.

Nevada held both Republican and Democratic Party primaries on Tuesday – with President Joe Biden projected to win his party’s ballot – mandated by a change in state law.

Both parties in Nevada used to hold caucuses to select their favoured presidential candidate, but in 2021 legislators said the primary process would allow for greater participation because people can vote by mail, or cast postal votes.

But the Trump-supporting Nevada Republicans is wildly distrustful of such measures, as is a swathe of the national party, and said it would ignore the primary and hold a caucus to allocate the state’s delegates.

It also decreed that any candidate who put their name forward for the primary could not enter its caucus.

Critics said while not illegal, the process was rigged to ensure a Trump win.

The caucus format, in which voters must attend an hours-long in-person event, more readily appeals to Trump’s fervent supporters.

The property tycoon could secure the Republican nomination by mid-March, having racked up an insurmountable lead in the delegate count.

But his own party and eventual rival Joe Biden have already acknowledged that he is the effective nominee.

Polls suggest another clear victory for Trump in South Carolina in just over two weeks – a defeat that could well push Haley to drop out, even though she has vowed to fight on.

The Nevada result is a further illustration of the grip Trump has on his party.

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He appeared earlier on Tuesday to have successfully torpedoed a bipartisan bill aimed at reinforcing the US southern border and amending immigration procedures.

Trump has pressured senators and House Republicans to vote down the bill that Biden said represented the “toughest set of reforms to secure the border ever,” as well as offering support to Ukraine and Israel.

“Because Donald Trump thinks it’s bad for him politically. Therefore … even though it helps his country, he’s not for it. He’d rather weaponise this issue than actually solve it,” Biden said.

The US presidential election in November promises to be tight, with polls showing Biden even or slightly trailing Trump, and suffering from the lowest approval ratings of any president for decades.

A poll by US broadcaster NBC published Sunday showed Trump leading Biden by 47 per cent to 42 per cent, within the poll’s margin of error but a shift from a Biden lead in mid-2023.

Americans are unenthusiastic about a rematch between the two, who many see as too old to be occupying the highest office in the land.