BISMARCK, United States (AFP) - White House hopeful Donald Trump claimed victory on Thursday in the Republican nomination race, while shrugging off criticism from the man he aims to replace, President Barack Obama, who blasted the billionaire's ignorance and arrogant attitude.

Trump vaulted past the threshold of 1,237 needed to win the party's primary race when a group of unbound delegates from North Dakota said they would back him.

The accomplishment caps an extraordinary rise by a political neophyte whose campaign was widely derided as a distraction and a publicity stunt last June, when Trump announced his candidacy.

Trump eventually swept 16 Republican rivals aside, and early this month was left as the last man standing when his remaining two challengers quit the race.

"The folks behind me got us right over the top from North Dakota," Trump told reporters in Bismarck, standing with some 15 unbound delegates from the midwestern state who committed their support to the real estate tycoon.

"I'm so honoured."

Several US media outlets, citing their own analysis of pledged delegates and unbound delegates who announced their commitment to Trump, said earlier on Thursday that Trump reached or surpassed the 1,237 mark.

The Republican Party will not make the delegate results official until its national convention in July, when delegates actually cast their votes for the nominee.

According to the US news agency the Associated Press, which first reported Trump crossing the threshold, Trump now has the backing of 1,238 delegates.

Trump was already the Republican presumptive nominee, following a spectacular and unlikely run for the White House that thoroughly upended American politics.

He now faces the daunting task of unifying skeptical Republicans, with turmoil continuing to dog his campaign as conservatives grapple with their party's direction.

Democrats have gleefully highlighted Republican anxiety about their nominee.

Speaking in Japan, Obama plunged into the fray, telling reporters that world leaders are "rattled" by some of Trump's policies.

"A lot of the proposals that he has made display either ignorance of world affairs or a cavalier attitude or an interest in getting tweets and headlines," Obama said.

Trump shot back, calling Obama "incompetent" and suggesting keeping world leaders guessing about Washington was just fine.

"We'll have great relationships with these countries. But if they're rattled in a friendly way, that's a good thing, John. Not a bad thing," he told a reporter.

The provocative Republican has struggled to win the support of key establishment figures, including House Speaker Paul Ryan, who have voiced concern about Trump's tone and his lack of policy specifics.

Ryan, the nation's top elected Republican, has yet to endorse Trump. They met two weeks ago to discuss ways to unify the party behind his presidential run, and spoke by phone late Wednesday.

But on Thursday, Ryan again stressed he wanted to see more unity in support of the candidate before endorsing him.

"What I'm most concerned about is making sure that we actually have real party unity, not pretend party unity," Ryan said.

The former reality TV star has dominated headlines since launching his presidential campaign with a mix of incendiary comments and policy stances seen as insulting Mexicans, Muslims and women among others.

He has proposed building a giant wall along the US border with Mexico to keep out illegal immigrants, and called for a ban on Muslims entering the United States.

Trump has also raised eyebrows by continuing to attack members of his own party.

On Tuesday, he assailed popular New Mexico Governor Susana Martinez - someone who could help him win over both Hispanics and women - saying she was not doing a good job as governor.

And the business mogul has shown his national political director the door just six weeks after hiring him.

Rick Wiley, who ran Wisconsin Governor Scott Walkers's ill-fated presidential campaign, "was hired on a short-term basis as a consultant until the campaign was running full steam," Trump's campaign said Wednesday.

Trump's likely Democratic rival in the general election, former secretary of state Hillary Clinton, is set meanwhile to clinch the nomination following the June 7 primaries, but she remains locked in a battle with challenger Bernie Sanders.

And while Trump has pivoted toward his likely matchup against Clinton, knocking her "bad judgment" in violating rules against using a private email account while secretary of state, he clearly reveled in seeing her struggle to put Sanders away.

"Here I am watching Hillary fight and can't close the deal. And that should be such an easy deal to close." With Clinton backing out of a debate with Sanders ahead of California's primary, Trump offered to fill the gap.

"I'd love to debate Bernie," Trump said, suggesting he would do so if they raised US$10 million for charity.

"Game on," Sanders said in a tweet.