Audrey Trujillo, who has called the 2020 election a ‘coup,’ is the G.O.P. nominee for New Mexico secretary of state.

Audrey Trujillo, a candidate who has espoused falsehoods about the 2020 election, promoted strict new voting policies and has shared racist and antisemitic comments on social media, has clinched the Republican nomination for secretary of state in New Mexico.

She ran unopposed in the primary, which was called by The Associated Press.

Ms. Trujillo, who carried out an unsuccessful campaign for state representative in 2020, is a member of the Trump-inspired “America First” slate of candidates for secretary of state and other offices, a national alliance forged by those still denying or doubting the legitimacy of the 2020 election.

She is the second candidate aligned with the group to win a G.O.P. nomination, after the primary victory last month of Doug Mastriano, the Republican nominee for governor in Pennsylvania, who would appoint the state’s top election official if he wins in November.

Another America First member, Kristina Karamo, was selected by Republican delegates at Michigan Republicans’ convention, nearly assuring her nomination later this year.

While Ms. Trujillo ran unopposed, many other races for secretary of state — a role overseeing elections in each state — have become hotly contested political battles. Across the country, the races are garnering record donations and attention, as Trump loyalists who continue to cast doubt on the 2020 election results seek to gain control over how elections are run.

Ms. Trujillo will face an uphill battle in November against Maggie Toulouse Oliver, the Democratic incumbent, given New Mexico’s tendency to tilt left.

But the national environment favors Republicans, and they have won statewide in the past. Dianna Duran, a Republican, was elected as secretary of state in 2010 and 2014, but she was forced to resign in 2015 after pleading guilty to embezzlement and money laundering charges.

Though she has not held public office before, Ms. Trujillo gained a modest following on her Facebook page, which is largely filled with pledges to rein in voting. In one livestream, Ms. Trujillo called for counties to hand-count every ballot, enact stricter voter identification requirements and limit absentee voting.

“This was a huge, huge — I’d say coup — to really unseat a president that actually had the best interests of Americans,” Ms. Trujillo said. She later added that New Mexico voting laws were so “lax” that “even our dogs can vote.”

She also drew criticism for old social media posts on a previous Twitter account — @AudreyTrueHero — that were discovered by The Albuquerque Journal last month. The account has since been deleted, but the newspaper wrote that one tweet included “an image of pharmaceutical executives with the Star of David — a symbol of Jewish identity — beside each face” with a caption reading “pick your poison.”

Another post appeared to poke fun at people who speak with Spanish accents.

Ms. Trujillo told the newspaper she was not “racist” and said that her account might have been hacked, or that she might have retweeted the posts without looking at them closely.

She did not respond to requests for comment from The New York Times.