Republican presidential candidate Nikki Haley turned a spotlight on Donald Trump's mental fitness Saturday, after the former president falsely accused her of failing to stop the violent assault on the US Capitol on 6 January 2021.

Trump, speaking Friday at a campaign event days ahead of New Hampshire's first-in-the-nation primary election, appeared to confuse Haley with then House speaker Nancy Pelosi.

Referring to the January 6 insurrection by a mob of his supporters, Trump, after saying his rival's name repeatedly, told a crowd: "Nikki Haley is in charge of security. We offered her 10,000 people -- soldiers, National Guard, whatever they want -- they turned it down. They don't want to talk about that."

Haley, Trump's top rival in the New Hampshire contest, pointed out not only was she not in charge of security at the Capitol, she was not even in office at the time.

"They're saying he got confused, he was talking about something else," the former UN ambassador and South Carolina governor said at a New Hampshire rally.

"The concern I have is, I'm not saying anything derogatory, but when you're dealing with the pressures of a presidency, we can't have someone else that we question whether they're mentally fit to do this."

Trump and other Republicans have repeatedly attacked 81-year-old President Joe Biden over his age and raised doubts over whether he has the mental acuity to serve a second term. 

The comments from Haley, who turned 52 on Saturday, were among the most direct challenges from a fellow Republican to the mental fitness of Trump, who is 77.

Haley has said political candidates over 75 should have to pass a test of mental competency, and she elaborated on that in a Fox News interview on Saturday.

"We need people at the top of their game. We need people that are focusing on national security... Do we really want them throwing out names and getting things wrong when they're 80 and having to deal with Putin and Xi and Kim and North Korea? We can't do that."

Trump's suggestion that Pelosi -- or Haley -- had turned down an offer of help while the Capitol was under siege also raised questions. 

The House committee that investigated January 6 said it found no evidence he had made such an offer.

Critics say Trump has increasingly shown signs of aging, and the former president himself addressed the question earlier in the week, repeating an account of how he once "aced" a test of acuity by correctly identifying animals such as a giraffe, a tiger and a whale.

But the issue appears to have done him little harm.

Far more voters, when polled, have expressed concern about Biden's age and fitness, and Trump -- who dominated in Iowa's presidential caucuses on Tuesday -- remains the overwhelming favorite among Republicans nationwide.