Despite another stinging defeat, this time on her home turf in South Carolina, Nikki Haley said on Saturday that she would forge ahead in the Republican primary race regardless of the daunting road ahead.

Speaking to several hundred supporters at her watch party in a ballroom in Charleston, S.C., Ms. Haley, the former governor of the state, cast herself as the voice for the “huge numbers” of Americans looking for an alternative to President Biden and former President Donald J. Trump.

She argued that Mr. Trump would be a losing candidate in November and that the nation could not afford four more years of his turbulence or what she described as Mr. Biden’s failures.

“I’m an accountant. I know that 40 percent is not 50 percent,” she said to some laughs, nodding to her share of the vote around the time she spoke. “But I also know 40 percent is not some tiny group.”

But she struck a more serious and determined tone in her remarks — so much so that as she began, it was difficult to tell whether she would indeed continue her bid, as she had pledged to do for weeks. But she soon put any speculation to rest.

“I said earlier this week that no matter what happens in South Carolina, I will continue to run for office,” she said. “I am a woman of my word.”

Ms. Haley’s loss in South Carolina follows a string of early defeats. Mr. Trump beat her in Iowa and New Hampshire in January, and she was outvoted by “none of these candidates” in a Nevada primary contest that didn’t include Mr. Trump. Still, she has pressed ahead with campaign events, bought more ads and rolled out leadership teams of elected officials and community leaders in states across the country.

In New Hampshire, Ms. Haley took 43 percent of the vote, and early in the South Carolina campaign, she and her allies said she needed to top that figure. But onstage on Saturday, she portrayed the 40 percent she had won at that point — a share that dropped slightly to 39 percent later in the night — as roughly the same.

She argued in her speech that the nation needed new leadership in the midst of “a world on fire.”

“It seems like our country is falling apart,” she said, adding that she was worried “to my core” for its future. “America will come apart if we make the wrong choices. This has never been about me or my political future. We need to beat Joe Biden in November.”

Ms. Haley’s supporters had expected a disappointing outcome in South Carolina, and as CNN projected Mr. Trump’s victory minutes after polls closed, it barely registered with the few dozen people who waited for her to take the stage. Within moments, the music was cranked back up. As Ms. Haley gave her short speech, the crowd broke out into chants of “Nikki, Nikki” and “U-S-A.”

The crowd at her party was much smaller in South Carolina than it had been at her gatherings in Iowa and New Hampshire. Mr. Trump was long seen as stronger in the Palmetto State, having consolidated the support of its Republicans, and he led her by more than 30 percentage points in some polls.

In recent weeks, crisscrossing the state on a bus tour, Ms. Haley had tried to remind voters of her accomplishments as governor and ramped up her attacks on Mr. Trump.

She called him too old and out of touch. She called him “unhinged” and a source of chaos. She went after what she described as his cozy relationships with dictators and his disrespectful remarks toward military members, including her own husband, Maj. Michael Haley, a National Guardsman. She argued that Mr. Trump would lead Republicans to ruin in November.

But in the homestretch, she seldom took questions from reporters and never did from voters. Her crowds were small and low-energy.

Nevertheless, Ms. Haley said she would travel to Michigan on Sunday as expected before the state’s Tuesday primary, and to states across the country ahead of Super Tuesday on March 5, when 15 states and one territory will hold contests.

“Today is not the end of our story,” she declared.

In interviews at Ms. Haley’s party, some of her supporters insisted that as long as she outperformed the polls and showed progress, she could rejuvenate her campaign.

Still, one backer, Ginny Bankov, 72, a former special education teacher, seemed stricken.

“I just thought something miraculous was going to happen today,” she said.