Nikki Haley on Saturday escalated her attacks on Donald J. Trump, directly criticizing his mental acuity for the first time a day after the former president appeared to confuse her for Nancy Pelosi, the former House Speaker, during his Friday night rally in New Hampshire.

In a news conference with reporters after her campaign event in Peterborough, N.H., Ms. Haley stopped short of calling Mr. Trump mentally unfit. But she did question whether he would be “on it” enough to lead the nation.

“My parents are up in age, and I love them dearly,” she said. “But when you see them hit a certain age, there is a decline. That’s a fact — ask any doctor, there is a decline.”

At his rally, the former president accused Ms. Haley of failing to provide proper security during the Jan. 6, 2021, attack on the Capitol, and connected her to the House committee that later investigated it. Ms. Haley, who was not holding a government role at the time of the attack, had been at home in South Carolina that day, according to campaign officials.

The former governor of South Carolina and a United Nations ambassador under Mr. Trump, Ms. Haley, 52, opened her presidential bid this year with calls for “new generational leadership” and mental competency tests for candidates who are 75 or older. Though she has continued to emphasize those calls throughout her candidacy, she has reserved her most pointed attacks about mental fitness for President Biden and Congress, which she calls “the most privileged nursing home in the country.”

The last time she came this close to knocking Mr. Trump directly was in October, after he criticized Israel’s prime minister, Benjamin Netanyahu, and referred to Hezbollah, the Iran-backed militant group, as “very smart.” Responding to those remarks, Ms. Haley said: “To go and criticize the head of a country who just saw massive bloodshed — no, that’s not what we need in a president.”

Since her election night speech after the Iowa caucuses, Ms. Haley has been sharpening her case against the former president, lumping Mr. Trump with Mr. Biden as backward-looking and barriers to an American revival. At her event in Keene, N.H., she criticized Mr. Trump on his leadership tone and asked the audience if they really wanted two “fellas” in their 80s competing for the presidency.

“I wasn’t even in D.C. on Jan. 6 — I wasn’t in office then,” she told the audience on Friday.

In a subsequent news conference, she suggested that the country was in too vulnerable of a state to have a leader who is mentally unfit.

“It’s a concern, and it’s what Americans should be thinking about,” she said.