Democratic presidential hopeful Beto O’Rourke’s campaign manager pressed Facebook, Twitter and Google on Friday to do more to stop the spread of online disinformation, raising concerns after scrambling this week to counter unsubstantiated internet postings that claimed one of the candidate’s supporters was responsible for a recent deadly mass shooting.

Jen O’Malley Dillon, Mr. O’Rourke’s presidential campaign manager, sent letters to the heads of the tech companies on the heels of their platforms giving air to the rumors, which claimed the gunman who killed seven people last month in West Texas was “a Democratic Socialist who had a Beto sticker on his truck.”

The posts were shared tens of thousands of times on both Facebook and Twitter, and the story “trended on Google, even though every single word of these posts were false,” according to Ms. Dillon.

“Our democracy depends on these platforms managing the crisis of disinformation. We’re aware they’ve all made efforts to improve. We are saying these efforts have been insufficient. They have to do better,” Ms. Dillon said on Twitter where she shared the letters. “This week it’s us, but every candidate is at risk of disinformation campaigns.”

“If there’s anything we can do to be helpful in preventing the spread of this kind of information against us, or any of our opponents, please let us know what we can do,” she wrote in the letters. “Because the future of our democracy depends on you getting this right.”

Representatives for Twitter and Google declined to comment on the campaign’s complaints, and Facebook did not immediately respond to a similar inquiry.

Danny Sullivan, Google’s public liaison for its search division, previously denied the company did anything to intentional promote the rumors and said that the story trended because of user interest.

Federal investigators have assessed that Russian internet users spread disinformation on social media during the 2016 U.S. presidential race in tandem with a state-sponsored effort to interfere in the U.S. electoral process, and companies across Silicon Valley has subsequently attempted to rein in abuse on their platforms ahead of 2020.

A former Democratic congressman for Texas, Mr. O’Rourke is among 10 presidential candidates set to participate in the next and third primary debate scheduled for September 12. Recently polling has placed him behind the current frontrunner, former Vice President Joseph R. Biden, and several other candidates seeking the Democratic nomination to compete against President Trump.

Eight people, including the perpetrator, died during last month’s shooting spree in the West Texas cities of Midland and Odessa. The gunman, 36-year-old Seth Aaron Ator, opened fire from a vehicle while driving, according to police.

Oscar Villarreal, a spokesman for the Texas Department of Public Safety, said there was no indication the shooter was linked to Mr. O’Rourke in any way, The Washington Post previously reported.

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