As Nikki Haley enters the final stretch of the Republican primary in South Carolina on Feb. 24, her presidential campaign on Tuesday unveiled a new national coalition aimed at making inroads with one group in particular: suburban women turned off by former President Donald J. Trump.

The group, the National Women for Nikki Coalition, includes more than 4,500 members in all 50 states and Puerto Rico, organizers said. Those members will ramp up the campaign’s get-out-the-vote initiatives, phone banking and other surrogate events in the coming weeks as Ms. Haley, the former governor of South Carolina, looks to continue her campaign beyond the next G.O.P. contest.

Though she faces long odds against Mr. Trump, Ms. Haley has signaled her intent to stay in the race at least through Super Tuesday, on March 5, when 15 states and one territory will vote on a Republican presidential nominee.

“They are a good representative of Republican women, suburban women, independent women who have had enough and know we can do better — so much better,” said Annie Dickerson, the coalition’s national co-chairwoman, adding that Ms. Haley was speaking for “the forgotten middle” of American politics.

Haley campaign officials say they are looking to turn out independents, new Republican voters and women in increasingly diverse and highly educated suburbs across the country that have trended away from the Republican Party in recent elections amid the rise of Mr. Trump. But as the former president maintains his grip on the Republican primary base, they face an uphill climb.

A poll from The New York Times and Siena College released in December found that 63 percent of female Republican primary voters supported Mr. Trump, despite his long history of misogynist remarks and sexual misconduct allegations. Ms. Haley had 12 percent support from that group. Other surveys show her garnering more support from men than women.

Ms. Haley’s female supporters tend to underscore her executive credentials and foreign policy experience more than her gender in celebrating her bid. Ms. Haley herself has tended to walk a careful line on that aspect of her identity, nodding to her high heels and jabbing at the “fellas” in the race, while rarely, if ever, mentioning that she is vying to become the first female president.

More recently, she has brought up that fact mainly to hit at President Biden and Vice President Kamala Harris, suggesting that Mr. Biden would not live to finish a second term and might not even be selected as the Democratic nominee.

“What I will tell you is there will be a female president of the United States,” she said to cheers during a bus tour stop on Saturday in Greenwood, S.C. “The hard truth is, it’s either going to be me or Kamala Harris.”