Nearly 2,200 flight attendants have reported reactions to the uniforms, Ross said. His letter called on American to stop issuing the uniforms; honor flight attendants' request for sick leave and reimburse them for medical expenses; and establish a $2 million fund to nail down what the issue is with the new outfits. It also claimed the airline wasn't taking "necessary steps" to address the problem swiftly.

"Personal health is so integral and critical to our Flight Attendant workforce, who must be able to work in a healthy manner and environment. To do so, our members need proper and safe uniforms," wrote the union's president, Bob Ross, in a letter on Wednesday to American's general counsel.

The uniforms, introduced in September, are causing a variety of issues, including "eye swelling, rashes, skin blistering," plus wheezing, headaches, and vertigo, claims a letter from the Association of Professional Flight Attendants, a union that represents more than 25,000 flight attendants at American.

New uniforms issued by American Airlines have thousands of flight attendants itching to get the old ones back, according to a grievance filed with the carrier.

The uniforms were rolled out to 70,000 employees, American Airlines told NBC News. The blazers and pants are a blend of wool, polyester, and spandex, while the shirts are 100 percent cotton, American said, adding that a cotton version of the uniform pieces is offered to those who are sensitive to wool.

American added that it has done three rounds of testing on the old uniforms, the new ones, and the packaging they came in. They have also opened a call center for flight attendants to report problems and are working with the flight attendant union to do a fourth round of testing.

"Our primary objective throughout the whole process has been to ensure that the uniform is safe for our team," Ron Defeo, a spokesman for the company, told NBC News via email. "We are confident our uniforms are safe, and we continue to encourage any of our team members who suspect a reaction to the uniform to contact their manager."

The uniforms are made by Twin Hill, a subsidiary of Tailored Brands, a retailer that includes brands such as Men's Wearhouse and Jos. A. Bank.

In announcing the new apparel in September, Tailored Brands said in a press release, "Elegant and modern yet reminiscent of a bygone era of luxury travel, the attire offers great style and design, high-quality performance and functionality that can take on the rigors of the job."

This isn't the first wrinkle for Twin Hill. The company was the subject of a class action lawsuit filed on behalf of hundreds of American Airlines flight attendants in 2012 who said they experienced numerous health problems as a result of their uniforms.

Twin Hill did not immediately respond to a request for comment from NBC News.