The only challenger to Donald Trump becoming the Republican Party candidate in the US election launched her sharpest attack yet on Tuesday, describing him as getting "more unstable and unhinged."

Nikki Haley, who trails far behind Trump in the polls, has defiantly refused to drop out of the race, fuelling anger from the Trump campaign as it seeks party unity in the face of the former president's multiple court cases.

"He's getting meaner and more offensive by the day," Haley said ahead of a primary vote in her home state of South Carolina on Saturday where she is forecast to suffer another crushing defeat by Trump.

"He's completely distracted, and everything is about him. He's so obsessed with his demons in the past that he can't focus on the future Americans deserve," she told supporters.

Haley, who was Trump's UN ambassador, again vowed to stay in the race despite some Republicans saying she is damaging their chances of defeating Democratic President Joe Biden in November.

"I have no fear of Trump's retribution," she said. "I refuse to quit."

Trump drew renewed criticism last weekend for saying he would encourage Russia to attack Nato countries who have not met their financial obligations.

"It's not normal to spend US$50 million dollars in campaign contributions on personal court cases," Haley said of Trump. "It's not normal to threaten people who back your opponent, and it's not normal to call on Russia to invade Nato countries."

Haley is more than 50 percentage points behind Trump in the Republican nomination battle, but says she has a better chance of beating Biden in the national election. (AFP)