The American fashion designer Willy Chavarria said he wanted to honor Mexican American culture when he created the Adidas Oaxaca Slip-On.

The shoe features a thick black sole from a 1990s Adidas hiking shoe and a woven black top that resembles that of a huarache, the traditional sandal made by Zapotec artisans in Oaxaca, Mexico.

“This to me is such a hybrid between my work and Adidas, and it’s just like the perfect combination,” he told the website Sneakers News last week. “It’s like literally one of the most classic Chicano references with the white sock.”

But when the shoe was released last week, political leaders in Mexico quickly accused Mr. Chavarria and Adidas of “cultural appropriation.”

President Claudia Sheinbaum of Mexico displayed an image of a pair of Adidas Oaxaca Slip-Ons at a news conference on Friday and said that Adidas and other companies were “usurping the creativity” of Indigenous communities.

She said that the government of Oaxaca had begun talks with Adidas aimed at reimbursing Indigenous communities for the use of their “collective intellectual property” and that Mexico was prepared to take legal action.

Mr. Chavarria, the son of an Irish American mother and a Mexican American father, issued an apology on Saturday, written in English and Spanish and addressed to “the people of Oaxaca.”

“The intention was always to honor the powerful cultural and artistic spirit of Oaxaca and its creative communities — a place whose beauty and resistance have inspired me,” Mr. Chavarria said. “The name ‘Oaxaca’ is not just a word — it’s living culture, it’s people, and it’s history.”

“I am deeply sorry that the shoe was appropriated in this design and not developed in direct and meaningful partnership with the Oaxacan community,” he added. “This falls short of the respect and collaborative approach that Oaxaca, the Zapotec community of Villa Hidalgo Yalalag and its people deserve.” Hidalgo Yalalag is a Oaxacan village where huaraches are made.

Adidas said in a statement that it “recognizes and values the cultural richness of Mexico’s Indigenous communities and the meaning of their artisanal heritage.”

“The Oaxaca Slip-On was inspired by a design from Oaxaca, rooted in the tradition of Villa Hidalgo Yalalag,” the company said. “We offer a public apology and reaffirm our commitment to collaborate with Yalalag in a respectful dialogue that honors their cultural legacy.”

Adidas did not respond when asked if the shoe was still being sold.

Mr. Chavarria’s work has often explored Mexican American culture, sexuality and immigration, drawing on his experience growing up in a farming community in California. His father was a migrant worker.

A former senior vice president at Calvin Klein, he told Sneaker News last week that he liked working with big brands such as Adidas because they helped him amplify his message of “human dignity.”

“It makes me very proud to be working with a company that really respects and uplifts culture in the most real way,” he said.

Salomón Jara Cruz, the governor of Oaxaca, said the shoe represented cultural “plagiarism.”

“The material and intangible cultural heritage of our people has to be recognized and respected,” he said on social media.

Mexican officials have a history of zealously defending traditional designs against what they consider inappropriate uses by outsiders.

Mexico’s culture ministry said in 2019 that it was surprised to find that a colorful chair made by the fashion house Louis Vuitton featured the designs of Mexican artists in Hidalgo. In response, Louis Vuitton said it was working with artisans in Hidalgo, “with the perspective of collaborating together to produce this collection.”

That same year, Alejandra Frausto, the cultural minister of Mexico at the time, wrote a letter to Carolina Herrera, the New York fashion brand, accusing it of using embroidery techniques and patterns from Mexican Indigenous communities in the brand’s resort 2020 collection. The clothing line featured floral and bird embroidery on strapless gowns, perforated leather coats and baby-doll cocktail dresses.

In response, Wes Gordon, the creative director of the label, told The New York Times that the company was considering what actions to take.

“We are going through a big social shift in how we talk about gender, culture and identity,” Mr. Gordon said. “These are important discussions to have. We take this very seriously.”