Former US president George W. Bush has launched into the caustic Republican nomination fray in support of his candidate brother Jeb, whose rival Donald Trump unleashed a new round of invective

at his challengers.

The political rhetoric in the presidential race has sharpened dramatically since the Iowa caucuses and the New Hampshire primaries earlier this month ahead of next Saturday’s crucial South Carolina primary.

The mini brawls were on the verge of spilling into open warfare ahead of the February 20 vote, the third statewide contest in the long battle for the Democratic and Republican nominations to run for president.

Jeb Bush, the onetime favourite seeking to build momentum in a state where his dynastic family remains popular, campaigned on Monday - President’s Day in the United States - with his brother, who was making his first appearance stumping for Jeb.

Trump rounded on the former president during Saturday’s debate in a bid to blunt any Bush progress, and he continued the assault Monday at a press conference, slamming George W, who was president during the September 11, 2001 terror attack on the World Trade Centre.

“So you had that. You obviously had the war which was a big mistake. I think few people would say the war in Iraq was a positive,” Trump said.

Trump also scolded Senator Ted Cruz, his current closest competitor, as “totally unstable” and a “liar” for attacking Trump’s earlier, liberal positions on abortion and health care.

And he repeated his threat to sue Cruz over his eligibility to be president, with Trump insisting that Cruz, who was born in Canada, is not a natural-born citizen as the US Constitution requires candidates to be.

Trump leads by a stunning 20 points over Cruz in South Carolina, known for its brutal political atmosphere. Senator Marco Rubio, who is seeking a resurrection after fizzling in New Hampshire and finishing fifth there, is third at 14.3 per cent, followed by a 10.5-per cent showing for Ohio Governor John Kasich, whose impressive second place New Hampshire finish was helping him surge here.

Bush is fifth at 10 per cent, with former neurosurgeon Ben Carson on 4.5 per cent.