Ahluwalia -- whose acting career has included roles in "The Grand Budapest Hotel," "The Darjeeling Limited" and "Inside Man" -- drew attention to his plight on social media, posting a photo of what he said was his canceled plane ticket.

In another post, the jewelry designer behind House of Waris said he might be late for New York Fashion Week because of the airline's decision.

"Don't start the show without me," he wrote.

Airline offers Ahluwalia an apology

Aeromexico offered an apology Tuesday, saying it "recognizes and is proud of the diversity of its passengers."

"We apologize to Mr. Waris Ahluwalia for the bad experience he went through with one of our security personnel," Aeromexico said in a statement.

The airline said it works to maintain strong security measures while respecting its passengers' cultures and beliefs.

The actor couldn't be immediately reached for comment on the apology.

Earlier, he had said wouldn't board a plane back to New York until the airline made a public apology and assurances that airport security personnel would receive Sikh awareness training and better instruction on how to screen passengers with religious headgear.

The Sikh turban: At once personal and extremely public

Sikh men have worn turbans since 1699 when the last living guru bestowed a unique Sikh identity based on five articles of faith. Among them were a steel bracelet signifying a reality with no beginning or end, a sword representing resolve and justice, and unshorn hair as a gift of God and a declaration of humility.

Some Sikh men don't wear turbans and beards; others say they stopped after being mistaken for Muslims and being targeted after 9/11.

Those who wear turbans shouldn't face discrimination, Ahluwalia said. Travelers should be taken into a private area if they're asked to remove their turban, he said, as U.S. Transportation Security Administration policy indicates.

Losing the Turban: Indian Sikhs at odds on essentials

Fashion world reacts

Ahluwalia, who didn't have any scheduled appearances on the runway this week, has become a well-known fixture in the fashion world -- in his home of New York and beyond.

His situation drew swift condemnation on social media and from the head of the Council of Fashion Designers of America.

Steven Kolb described Ahluwalia's treatment as "outrageous" and called him "overall the nicest guy in our industry."

"He is a front-row fixture of Fashion Week, and not to have him here is unfair to him on so many levels," Kolb said. "We support him in his decision for wanting to make this a teachable moment, and I have a lot of respect for him."

'We have to be vigilant'

Ahluwalia said he has had brushes with bigotry before. In 2013, a Gap holiday ad with him drew widespread attention after someone defaced it in a New York subway station.

"Make Love" was crossed out to read "Make Bombs." Beneath that, someone scrawled, "Please stop driving TAXIS."

The company was quick to replace the ad and double down on its campaign, making the photo its background image on Twitter and Facebook and releasing a statement saying Gap "is a brand that celebrates inclusion and diversity."

That "was a great example for corporate responsibility," Ahluwalia said, "but this is the exact opposite of that.

"I didn't ask to be a public face or voice of a religion. Sikhs have been in (the United States) for over 125 years," he said. "I just want to make and create art."

But Ahluwalia said he knew he needed to take a stand.

"I'm not sitting here angry at Aeromexico. Everyone makes mistakes. I've made mistakes," he said. "But what makes us different is how we collect and respond and react to the mistakes we make. They did not know. I cannot blame them for that, but ignorance and fear is the flag humans carry, and we have to be vigilant to fight that."