By Jacob Gallagher, Khadeeja Safdar and Sharon Terlep

Companies from Adidas AG to Estée Lauder Cos. face pressure from employees to do more to confront racism and promote diversity, as social activism over the killing of George Floyd moves deeper into the workplace.

Following the killing of Mr. Floyd last month, Adidas like many brands took to social media to speak out against racism. Yet, some black employees at the company's U.S. offices say the corporate culture at the German company is far from equitable. Those sentiments were echoed at other companies in recent days from cosmetics sellers to media outlets.

Recent statements "don't necessarily align with how anybody feels internally about the things that [Adidas] does to help support black people," said Aric Armon, an Adidas footwear designer in Portland, Ore.

On Sunday, Mr. Armon publicly shared a story on Instagram, where he said a former Adidas co-worker called him the N-word during a trip to the Super Bowl in Miami this February. The former co-worker said he wouldn't comment on the post until he meets with Mr. Armon and Adidas's human-resources department.

Adidas hires black people to help it "connect with the black consumer," said Mr. Armon, who has worked at the company for seven years. In his experience, though, it has been difficult for black people to advance at Adidas. "It really becomes evident that we're just kind of there for our insights and not necessary for leadership," he said in an interview Monday.

Adidas declined to comment about individual employees or executives. "We recognize that we have not done enough, and we are dedicated to doing more," the company said in response to the general employee backlash. "We are close to finalizing our commitments to ensure our people, most importantly our black employees, are heard, supported and involved in solutions."

Adidas, Nike Inc. and Under Armour Inc. for years have faced complaints from some employees that these global giants profit from marketing black sports stars and selling sneakers and other products to black communities, but have few people of color or women in their leadership ranks.

Neither Adidas's six-person executive team nor its 16-person board of directors includes a black member. None of the 10 executives currently listed on Nike's executive leadership website are people of color. Estée Lauder has two black women among its 14-person executive team and one black director on its 16-member board.

Adidas declined to provide details on the diversity of its broader leadership; Nike said several senior leaders are from underrepresented groups. Late Monday Estée Lauder detailed plans to improve its diversity and support the black community.

Last week, a group of black Adidas employees sent a presentation called "Our State of Emergency" to executives, calling for the company to increase representation of black and Latino employees to 31% of every level of the organization by the end of 2021.

The document, which was earlier reported by Footwear News, also called on the company to give $50 million in global sales a year to black U.S. communities and help raise money for nonprofits serving those communities.

Adidas said it stands against racism and was "deeply saddened by what we see happening to our black community in America." The company said its executives in North America and its German headquarters attended educational sessions last week to understand and learn how to lead through the aftermath of Mr. Floyd's killing.

At an all-employee meeting last August at the Boston headquarters of Reebok, which is owned by Adidas, Karen Parkin, head of Adidas's human resources, said racism was "noise" that is only discussed in America, and that she didn't believe the brand had an issue with racism, according to Aaron Ture, the manager of fashion footwear collaborations at Reebok, who was at the meeting. This event occurred two months after a New York Times article detailing racial inequalities at Adidas.

Ms. Parkin didn't immediately respond to a request for comment.

Julia Bond, an assistant designer in Adidas's men's originals category, said she is the only black person on her team of more than 20 people. In August, shortly after she was hired, her team received a design inspiration packet from the brand's Herzogenaurach, Germany, headquarters that included an image of an Asian man wearing a T-shirt with the Confederate battle flag, she said.

The photo was "painful to look at," said Ms. Bond. "I don't even know if [my co-workers] realized how many of my ancestors died because people wave that flag."

Last week, Ms. Bond sent a letter to Adidas's North American leadership team that called for the company to "issue a public apology for the racism and discrimination that they have openly enabled and perpetuated across the brand."

In a letter to employees last week, Nike Chief Executive John Donahoe said he was creating a task force, run by Craig Williams, president of the Jordan brand, to decide how the company will "engage on racial diversity" and where to spend $40 million that it is committing to support the black community over the next four years.

Nike, which faced internal protests in 2018 over diversity in its leadership and workplace culture, has said that black vice presidents represented 9.9% of its U.S. total in 2019. Its highest-level black executive, Trevor Edwards, resigned in 2018 amid that turmoil.

Nike said there are diverse senior leaders throughout the company, including the presidents of its Jordan and Converse brands, and the vice president of strategy. Three of Nike's 13 board members are people of color, after the company added members since 2018.

"In the past year, Nike increased VP-level representation for U.S. underrepresented groups by two percentage points to 21%. While this is good progress, we know there is more work to do," a Nike spokesman said.

The calls for internal change go beyond sportswear makers. A group of Estée Lauder employees in recent days have called for removing Ronald Lauder from the board of the cosmetics company founded by his mother. The employees object to Mr. Lauder's fundraising and support for President Trump. They also are asking the company to donate $5 million to the black community, up from the $1 million planned.

Chairman William Lauder and Estée Lauder CEO Fabrizio Freda, in a memo to employees reviewed by The Wall Street Journal, said individual donations don't represent the company's views. "Our employees have the right to vote for whomever they choose, to engage in their communities and to express their views," the letter said. Ronald Lauder declined to comment through a company spokesperson.

Estée Lauder promised its portfolio, which includes Clinique and MAC, will fit the needs of black consumers. The company also pledged to donate $10 million over the next three years to racial and social justice organizations and improve access to education.

A.J. Stabe, an Estée Lauder art director, was among those to sign an online petition calling for Ronald Lauder's ouster. He said the issue has been galvanizing for employees because the company's message of inclusion and social justice is at odds with Mr. Trump's policies.

"We as employees are trying to affect this change in any way we can," Mr. Stabe said.

On Monday, digital news organization Refinery29 co-founder Christene Barberich said she would step aside as editor in chief after former staffers took to Twitter to complain about the treatment of black employees. The Vice Media-owned outlet last week said it was undertaking a comprehensive assessment.

"I've read and taken in the raw and personal accounts of black women and women of color regarding their experiences inside our company," Ms. Barberich wrote in an Instagram post. "We have to do better, and that starts with making room."

Write to Jacob Gallagher at Jacob.Gallagher@wsj.com, Khadeeja Safdar at khadeeja.safdar@wsj.com and Sharon Terlep at sharon.terlep@wsj.com