Former President Donald J. Trump continued his aggressive attacks on Nikki Haley Saturday, insinuating at a rally in South Carolina that her husband, a National Guardsmen, left for a deployment in order to escape her.

“What happened to her husband? Where is he?” Mr. Trump said to a crowd in Conway, S.C. “He’s gone.”

He then paused, before adding suggestively: “He knew. He knew.”

Mr. Trump’s comments, made in Ms. Haley’s home state two weeks before its Republican primary, are a stark turn in an escalating barrage of attacks on her as he looks to knock her out of contention in the Republican primary. Though he has for weeks criticized Ms. Haley’s political views and made vague swipes claiming she lacks a presidential temperament, he has refrained from making specific personal smears.

Later in his speech in South Carolina, Mr. Trump — who for months has referred to Ms. Haley as “birdbrain” without offering an explanation — called her “brain dead” while criticizing her position in national polls.

Ms. Haley’s campaign did not immediately respond to a request for comment, but she posted a comment on X that referred to the absence of her husband, Michael, from the campaign trail.

“Michael is deployed serving our country, something you know nothing about. Someone who continually disrespects the sacrifices of military families has no business being commander in chief,” she wrote.

Ms. Haley’s husband is currently serving a voluntary, yearlong deployment in Africa that began last June. He is stationed at Camp Lemonnier, a sprawling military base in Djibouti. Mr. Trump’s comments followed an increasing focus on the topic among right-wing media personalities who are backing the former president.

Though he is currently overseas, Mr. Haley has been a regular presence of Ms. Haley’s messaging in her bid for the nomination. In her stump speech, she describes him as one of her reasons for running, often describing his struggles after returning from a war zone and suggesting that his work has informed her views on foreign policy and immigration

“The other candidates are sitting there saying I’m a warmonger,” she said last year at a community center in Treynor, Iowa, where a restored U.S. Army helicopter hangs in tribute to the 114th Aviation Company at Vinh Long in South Vietnam. “Are you kidding? My husband’s in the military. The last thing I want him to do is go fight. This is about preventing war. We should always be looking to prevent war.”

In interviews with voters in Iowa, New Hampshire and South Carolina, Mr. Haley has often come up organically as a reason for their support. Wives and mothers with spouses or children in the military tend to connect with the tough experience of worrying about and rarely seeing their loved ones. Retired military officers see her as someone who might better understand their plight.

Both Ms. Haley and Mr. Trump share, to some extent, the absence of their spouses on the campaign trail. Melania Trump, the former first lady, has not joined Mr. Trump at events, nor has she been at his side during his court appearances.

Mr. Trump’s attacks on Ms. Haley, the former governor of South Carolina, came as his campaign has for weeks pursued a strategy meant to humiliate her in her home state.

On Saturday, Mr. Trump once again said that he appointed her to become ambassador to the United Nations only in order to clear the way for her successor, Gov. Henry McMaster, who endorsed Mr. Trump shortly after he began his 2024 campaign.

Ms. Haley has also ramped up her criticism of Mr. Trump, particularly as her path toward the Republican nomination has narrowed and she has become his only major competitor. Recently, she has attacked Mr. Trump in light of the special counsel report questioning President Biden’s mental acuity over his handling of classified documents.

At campaign stops in South Carolina on Saturday she doubled down on her urgent calls to Republicans to not overlook Mr. Trump’s own age and mental challenges, warning without evidence that Democrats appeared to be looking to replace Mr. Biden and that Republicans should “wake up,” too.

In Newberry, S.C., her campaign staff passed out mock mental competency worksheets with questions that the sheets suggested Mr. Trump and Mr. Biden would not pass. Ms. Haley told reporters that she had not taken the test but that she would be happy to do so.

The Haley campaign also paid for a mobile billboard to troll the former president around the Myrtle Beach area, including near his event in Conway.

Mr. Trump has also called for cognitive tests for presidential candidates, part of his strategy to attack Mr. Biden’s mental acuity for months.

On Saturday, he turned Ms. Haley’s attack back on her. “I don’t think Nikki would pass the test,” he said. “I really don’t.”

Maggie Haberman contributed reporting from New York.