By Sahil Patel, Katie Deighton and Ann-Marie Alcántara

The chief executive of Ben & Jerry's Homemade Inc. said the ice-cream brand is considering joining other companies in boycotting advertising on Facebook Inc.'s platforms while pushing more of its media partners to take further action on issues concerning systemic racism and social reform.

"What they've been doing is not fully right with our values, period," said Matthew McCarthy, the Ben & Jerry's CEO, on Facebook's policies regarding toxic content on its platforms. "The reality is, anything that's right for the business, but wrong for our values, is wrong."

Mr. McCarthy made his remarks Monday during the CMO Network Summit hosted by The Wall Street Journal's CMO Network.

Civil-rights groups including the Anti-Defamation League and the NAACP last week called for big advertisers to pull spending from Facebook for July to protest what they say is the company's failure to make its platform a less hostile place.

Many large digital platforms are facing pressure over how they handle content on their sites, pressure that increased amid the protests spurred by the killing of George Floyd and other issues of police brutality.

Carolyn Everson, vice president of Facebook's Global Business Group, said in a statement that the company remains focused on removing hate speech from its platforms and is in conversations with civil-rights groups and marketers about how they can work together to be a force for good.

Mr. McCarthy said Facebook is just one platform, despite its size, and that he will be seeking broader changes.

"What we want to do is to try to make ourselves right at Ben & Jerry's -- we always aspire to do the right thing. And we want our partners to do the same thing," he said. "So to me, it's not just about signing on to boycott, which certainly, we may do. It's about what are the actions that we'd like to see happen so that we can collaborate with partners who want to progress the change that we support."

Others who spoke at the CMO Network Summit said they were pushing for change without boycotts.

Ben & Jerry's parent Unilever PLC tries to influence Facebook in the course of doing business with it, but isn't considering a wholesale boycott, said Luis Di Como, the company's executive vice president of global media.

"Walking away is not the solution at this stage," he said. Unilever continually adjusts its investment in favor of platforms that make progress scored against its "Responsibility Framework," Mr. Di Como said.

A Ben & Jerry's spokesman said Unilever's corporate approach wouldn't affect its own decision on advertising with Facebook. The ice-cream brand operates as an independent subsidiary and has taken positions that differ from the parent company's before, he said. Unilever didn't immediately respond to a request for comment.

The social networks should develop more parameters around how users interact, said Deborah Wahl, global chief marketing officer at General Motors Co. Although the auto maker will follow its beliefs, it isn't going to mount a public confrontation, she said.

"At GM, we're not going to engage in big statements about platforms and such," Ms. Wahl said.

Several brands have taken up the call for a boycott.

Apparel brand The North Face said Friday it would to stop its advertising on Facebook and its Instagram subsidiary through the end of July. "We hope they will reconsider their policies and will re-evaluate our position in the next 30 days," a spokeswoman for North Face parent VF Corp. said.

In a tweet, the clothing company Patagonia Inc. said Sunday that it would also pull all ads on Facebook and Instagram through at least the end of July "pending meaningful action from the social media giant."

Last week, the ad agency 360i, part of Japanese ad giant Dentsu Group Inc., emailed clients encouraging them to support the civil rights groups' call for an ad boycott of Facebook. Ben & Jerry's is a client of 360i.

In its email, 360i said it "believes any social platform that earns profits by amplifying the voices of their community must have a zero-tolerance policy for hate."

Ben & Jerry's is known for being vocal about its support of social issues including criminal-justice reform, and backed the Black Lives Matter movement before the current unrest. But its executives, including Mr. McCarthy, have said the company needs to improve the representation of black employees within its corporate headquarters, franchise network and supply chain.

Write to Sahil Patel at sahil.patel@wsj.com, Katie Deighton at katie.deighton@wsj.com and Ann-Marie Alcántara at ann-marie.alcantara@wsj.com