By Sahil Patel

Tuesday's statement from Ben & Jerry's Homemade Inc. put the killing of George Floyd while in police custody in stark terms.

"What happened to George Floyd was not the result of a bad apple; it was the predictable consequence of a racist and prejudiced system and culture that has treated Black bodies as the enemy from the beginning," the ice-cream brand owned by Unilever PLC said, in part.

But the statement was only part of a wide rush by marketers to express support for protesters angry about Mr. Floyd's death and, more broadly, racial inequality. Now the question is what brands will do beyond sympathize, advocates and others say. And donations aren't the end of the conversation.

Marketers have corporate social responsibility and diversity commitments to meet, said Doug Rozen, chief media officer of Dentsu Inc.-owned ad agency 360i. "But that does not mean your brand needs to only match those commitments," he said. "Brands need to be more proactive in the diversity conversation and not just reactive."

The civil-rights group Color of Change has called on Nike Inc., which released a video encouraging people to fight racism, and other companies to go beyond statements and improve the wages and working conditions of their employees.

"These messages of support mean nothing without taking action to support their Black employees," spokespeople for Color of Change said.

Companies say they are trying to do better.

Nike on Friday announced a $40 million commitment over four years to support organizations focused on social justice, education and racial inequality in the U.S. In addition, basketball legend Michael Jordan and Nike subsidiary Jordan Brand said they will donate $100 million over the next 10 years to those causes.

In a statement, a Nike spokeswoman said the company remains committed to equal pay across genders and races and ethnicities, defined as those who "undertake the same work at the same level, experience and performance." Based on those parameters, the company's internal data show that for "every $1 earned by white employees in the U.S., those from under-represented groups earned $1."

On diverse hiring practices, the apparel giant increased vice president-level representation for underrepresented groups in the U.S. by two percentage points, to 21%, in 2019. "While this is good progress, we know there is more work to do," the spokeswoman said.

Ben & Jerry's has long spoken up about social issues, and backed the Black Lives Matter movement before the current unrest.

Its foundation donated $3 million in 2019 as part of employee-led grant programs supporting social and environmental justice in the U.S., the company said. Ben & Jerry's also devotes 10% to 20% of its annual marketing spending to promote progressive groups or causes, it said. It ran Facebook ads last year promoting its Pecan Resist ice cream flavor, for example, which raises money for advocates including Color of Change.

But the Vermont-based company has its own problem areas, particularly the lack of diversity in its workforce, said Chris Miller, global activism manager at Ben & Jerry's.

"We have one black person at corporate headquarters," Mr. Miller said. "Our demographics, internally, don't look dissimilar to the community in which it resides."

Ben & Jerry's is undergoing an internal review, which was in the works prior to the protests, to examine and improve diversity across the company, its franchise network and supply chain, Mr. Miller said.

Some other companies said they recognize the need for more than one-time gestures, even financial ones.

"It's decades of systematic and structural issues that keep the most disadvantaged and underprivileged people down," said Minjae Ormes, chief marketing officer at Visible, a prepaid mobile phone carrier owned by Verizon Communications Inc. "And a problem of that magnitude requires an equally systematic approach to creating consistent and enduring impact."

Visible has an ongoing company program called Visible Connect, through which it donated $400,000 in grants in 2018 and 2019 to nonprofits that are closing some type of opportunity gap in areas ranging from early childhood education to mental health, Ms. Ormes said. One recipient of the program is Good Call NYC, which connects protestors arrested in New York City with legal resources.

Insurance giant Progressive Corp. has pledged $1 million to the Equal Justice Initiative in support of the nonprofit's efforts to end mass incarceration, excessive punishment and racial injustice, said Tricia Griffith, the company's chief executive.

Progressive's efforts in recent years have also focused on hiring a more diverse workforce, the company said.

"We must and will do more," Ms. Griffith said.

Brands are more open to conversations and taking action on race issues, but only a minority of them have pledged contributions, said Kieley Taylor, global vice president of social at WPP PLC-owned GroupM. "But it does feel like a tipping point; advertisers who are being more outspoken in their actions are [indirectly] helping others feel more comfortable that they can too," she said.

Brands need to do more than "virtue signaling," said Michael Natenshon, chief executive of 10-year-old casual clothing company Marine Layer Inc., which is donating $10,000 to four groups including the NAACP and the Bail Project, a nonprofit that offers bail assistance to low-income individuals.

Marine Layer's business was hurt by the closing of retail stores due to the coronavirus pandemic, but it hopes to contribute more as business returns, he said.

Marine Layer plans to hire Adaway Group, a black-owned consultancy, to determine where it falls short in its own hiring practices; approximately 10% of the company's roughly 275 employees identify themselves as black or African-American.

"We consider ourselves an equal-opportunity employer, but if we go about it that way without thinking about race or ethnicity in that process, then we are being passive," Mr. Natenshon said.

Write to Sahil Patel at sahil.patel@wsj.com