The former South Carolina governor is just the second Republican to seek the party's backing to challenge Democratic President Joe Biden, 80, who is expected to seek reelection next year.
Haley, the daughter of Indian immigrants, hit on a long list of Republican concerns in her speech in Charleston, including border security, spending bills authorized by Democrats in Congress and the recent incursion into U.S. airspace of what U.S. security officials say was a Chinese spy balloon.
"We are more than ready for a new generation to lead us into the future," Haley, 51, told a crowd of several hundred supporters.
Haley only mentioned Trump, 76, once during her speech, as she highlighted her foreign policy experience as the former president's top U.N. envoy and vowed tough action against U.S. adversaries such as China.
But she will likely face a large field of competitors for the Republican nomination, with Florida Governor Ron DeSantis, former Vice President Mike Pence and her fellow South Carolinian U.S. Senator Tim Scott seen as potential rivals.
Trump said in an interview with Fox News Digital that he was glad she was running.
"She should do what she wants to do and not be bound by the fact that she said she would never do it," Trump said, referring to comments Haley made in 2021 saying she wouldn't challenge him.
Haley faces an uphill climb: a Reuters/Ipsos poll released on Tuesday found that just 4% of registered Republicans supported her.
Trump received support from 43% of registered Republicans in the poll conducted from Feb. 6-13, while 31% said they supported Florida Governor Ron DeSantis, who is expected to launch a campaign but has not yet done so.
Biden, who has not formally launched his reelection bid, faces no major Democratic challenger.
But it is early in the 2024 cycle. With more than 20 months remaining until Americans cast ballots, Haley and her rivals have ample time to build their public profiles and raise money.
One rally attendee, Carol Baker, 83, said she liked Trump's policies but thinks Haley will be able to implement them in a less contentious and more effective fashion.
"His (policies) were wonderful, but his personality got in the way," she said after Haley's remarks.
Haley also criticized what she described as a culture of negativity in the United States.
"A self-loathing has swept our country. It's in the classroom, the boardroom and the back rooms of government. Every day we're told America is flawed, rotten and full of hate," Haley said. "The American people know better. My immigrant parents know better. And take it from me, the first minority, female governor in history: America is not a racist country."
South Carolina Republican Ralph Norman, a member of the U.S. House of Representatives' conservative Freedom Caucus who was a staunch Trump ally during his presidency, endorsed Haley for president and praised what he described as her calm demeanor.
"But folks, don't let that calm demeanor fool you. Nikki will be a leader with an iron fist in a velvet glove," he told Haley supporters at her Charleston campaign event.
Haley said that if Republicans were tired of losing, they should put their trust in a new generation.
"We've lost the popular vote in seven of the last eight presidential elections. Our cause is right, but we have failed to win the confidence of a majority of Americans," Haley said.
Haley received national attention in 2015 when, as governor, she called for the removal of the Confederate battle flag from the grounds of the state capitol after the murder of nine black churchgoers by white supremacist Dylann Roof.
But she later drew criticism in a 2019 interview when she said the flag represents "service, sacrifice and heritage," adding that its meaning had been hijacked by Roof.
If she wins, she would be the first non-white or female Republican presidential nominee.