Shareholders in Home Depot and the advertising giant Omnicom have filed resolutions asking the companies to investigate whether the money they spent on advertisements may have helped spread hate speech and misinformation.

The resolutions were filed in November but were not made public until Monday. They were coordinated by Open MIC, a nonprofit group that works with shareholders at media and technology companies.

The two shareholder resolutions, which used similar language, asked Home Depot and Omnicom to commission independent investigations into whether their advertising policies “contribute to the spread of hate speech, disinformation, white supremacist activity, or voter suppression efforts.”

“Advertisers are not passive bystanders when they inadvertently finance harm,” the resolutions said. “Their spending influences what content appears online.”

Omnicom manages $38 billion a year for its marketing clients, while Home Depot advertises heavily on Facebook, according to the filings.

Misinformation about voter fraud, spread in large part through online platforms, contributed to a siege of the U.S. Capitol on Jan. 6 by a mob fueled by debunked conspiracy theories about a stolen election — theories promoted by President Trump and his allies.

These days, companies devote more than half their spending on global marketing to digital ads. Because many of those ads are placed by third-party vendors using automated algorithms, often with little human oversight, companies are frequently unaware when their ads show up on websites that peddle misinformation.

A report last week by NewsGuard highlighted the problem. The company evaluates the trustworthiness of online news outlets, and was started by Steven Brill, the founder of the magazine The American Lawyer, and Gordon Crovitz, a former publisher of The Wall Street Journal. The report found that 1,668 brands ran 8,776 unique ads on 160 sites that published misinformation about the 2020 election.

The outlets flagged by NewsGuard include The Gateway Pundit, Infowars, Newsmax and websites affiliated with the right-wing pundits Sean Hannity, Dan Bongino and Rush Limbaugh.

Companies have struggled in recent years to reach potential customers while making sure their online ads do not appear close to dubious, salacious or potentially harmful content. AARP, which was mentioned in the NewsGuard report as one of the companies that had placed ads on sites promoting false election claims, said that, despite rigorous monitoring procedures, some ads slipped through the cracks.

“We follow strict ad placement protocols, but no system is 100 percent foolproof,” Martha Boudreau, an AARP executive vice president, said in a statement.

An AARP internal review found that “a tiny portion” of its ads, less than 1/100th of 1 percent, appeared on the sites flagged by NewsGuard, Ms. Boudreau added.

Matt Skibinski, the general manager of NewsGuard, said companies should treat sites that publish misinformation the same way they treat sites that promote behaviors that do not align with their corporate values or that publish content they do not want to be associated with.

“At many brands, there is somebody whose job it is to make sure they don’t place ads in what they would call unsafe or unsuitable environments, and that includes violence, pornography and gambling,” Mr. Skibinski said. “We need the industry to start seeing misinformation in that category — of creating real-world harm.”

NewsGuard reported that Procter & Gamble ads had appeared on The Gateway Pundit, one of the sites it called out for publishing election misinformation. In an email, Procter & Gamble said it had not intentionally advertised on the site. Erica Noble, a Procter & Gamble spokeswoman, said that when the company’s ads are placed on a site that does not meet its standards, it acts quickly to remove them.

“These are all standards that were in place well before the horrific events of Jan. 6, but we appreciate they take on renewed importance now,” she said.

Since the Capitol siege, social media platforms have cracked down. Facebook, which weathered an advertiser boycott during the summer over misinformation and hate speech, barred Mr. Trump from its platform and said it would remove content related to the “Stop the Steal” movement. Twitter took similar action.

Omnicom said in a statement that it “is committed to ensuring our clients’ ads do not appear next to harmful content on social media platforms” and pointed to an effort it spearheaded in the summer to audit and track platforms’ ad placement practices.

Home Depot said in a statement that it was “saddened and outraged by the violent attack on the U.S. Capitol and our lawmakers” and “disgusted” by malicious content on social media.

“We’re addressing the proposal through the appropriate process,” said Sara Gorman, a spokeswoman.