Nikki Haley has questioned Donald Trump's mental capacity to serve a potential second term in the White House.
Ms Haley, 52, made the comments after Mr Trump, her Republican rival, appeared to confuse her with former House Speaker Nancy Pelosi at a rally in Concord ahead of the New Hampshire primary on Tuesday.
The former president, 77, implied the then speaker did not have any security when the 6 January insurrection happened in Washington DC, calling her a "birdbrain".
He said on Friday: "Nikki Haley, you know, they, do you know they destroyed all of the information, all of the evidence, everything, deleted and destroyed all of it.
"All of it, because of lots of things like 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. These are very dishonest people."
Mr Trump has previously criticised Ms Pelosi for refusing additional security he offered her on 6 January 2021.
Conspiracy theory, misinformation and an alternative truth, three years on
In Keene, New Hampshire, on Saturday, Ms Haley commented on the ages of both Mr Trump and President Joe Biden, 81.
"We see that Biden has changed so much in two years.
"But last night, Trump is at a rally and he's going on and on, mentioning me multiple times as to why I didn't take security during the Capitol riots.
"Why didn't I handle 6 January better? I wasn't even in DC on 6 January. I wasn't in office then."
She added: "They're saying he got confused, that he was talking about something else, he's talking about Nancy Pelosi.
"The concern I have is - I'm not saying anything derogatory - but when you're dealing with the pressures of the presidency, we can't have someone else that we question whether they're mentally fit to do this. We can't."
Ms Haley, a former UN ambassador, came third behind Mr Trump in the Iowa caucus on Monday - the first event in the election calendar.
She refused to take part in any debates in New Hampshire, the second stop on the road to candidate nomination, unless Mr Trump took part, which he has declined to do so far.
The Republican contender says she would legislate to ensure anyone in federal office over the age of 75 takes a mental competency test.