X, the social media service formerly known as Twitter, sued Media Matters in federal court on Monday after the advocacy organization published research showing that ads on X appeared next to antisemitic content.

A post last week from Elon Musk that endorsed an antisemitic conspiracy theory, which he wrote a day before the Media Matters research was published, kicked off an advertiser exodus, with major brands like IBM, Apple, Warner Bros. Discovery and Sony pausing their spending on the platform.

X has rejected Media Matters’ findings, saying they were not representative of a regular user’s experience on the platform. On Friday, Mr. Musk promised a “thermonuclear lawsuit” against Media Matters and its backers.

The lawsuit, filed in U.S. District Court for the Northern District of Texas, claims that Media Matters tried to damage X’s relationships with advertisers. “Media Matters has manipulated the algorithms governing the user experience on X to bypass safeguards and create images of X’s largest advertisers’ paid posts adjacent to racist, incendiary content, leaving the false impression that these pairings are anything but what they actually are: manufactured, inorganic and extraordinarily rare,” lawyers for X wrote in the complaint.

Media Matters did not immediately respond to a request for comment on the lawsuit. Angelo Carusone, the president of the organization, said on Friday that Mr. Musk had confirmed that ads ran on X alongside pro-Nazi content.

“Far from the free speech advocate he claims to be, Musk is a bully threatening a meritless lawsuit in an attempt to silence reporting that he even confirmed is accurate,” Mr. Carusone said on Friday. Media Matters would prevail in a lawsuit, he added.

On Monday night, Ken Paxton, the Texas attorney general, also announced that his office would open an investigation into Media Matters for “potential fraudulent activity.”

Brands have been hesitant to advertise on X since Mr. Musk bought the company a year ago and said he would relax its content-moderation policies. X has sought to woo hesitant advertisers back to the platform, an initiative that has been overseen by Linda Yaccarino, a longtime advertising executive who became X’s chief executive in June.

But Mr. Musk’s post on Wednesday, in which he agreed with a post from an X account accusing Jewish communities of pushing “hatred against whites that they claim to want people to stop using against them,” was a setback.

“You have said the actual truth,” Mr. Musk replied to the post.

Jewish groups quickly condemned the statement that Mr. Musk endorsed, likening it to the “Great Replacement Theory,” a conspiracy theory that claims minorities are replacing white European populations as part of a coordinated effort by Jewish people. The White House condemned Mr. Musk’s remark, and top-tier brands quickly pulled their advertising off X.

Mr. Musk said in a post to X on Sunday that claims that he was antisemitic were untrue. “Nothing could be further from the truth,” he wrote.

In its lawsuit, X asked the court to order Media Matters to take down its published research. The lawsuit also seeks unspecified monetary damages and lawyers’ fees.

Ms. Yaccarino said in a statement that the X account that Media Matters had used in its research was the only account that saw some of the ads next to the antisemitic posts in question. In the case of Apple, its ad was placed next to an antisemitic post and viewed by another user, she added.

“If you know me, you know I’m committed to truth and fairness,” Ms. Yaccarino said in a post on X. “Data wins over manipulation or allegations. Don’t be manipulated. Stand with X.”

During an all-staff meeting on Monday, Ms. Yaccarino said she had discussed the issue with advertisers and was committed to defending X, according to audio of the meeting heard by The New York Times. In those conversations, some advertisers had asked her to be more communicative about problems to get in front of them, and to share more data about how ads are displayed on the platform, she said.

“We want to work with all of our partners who stand with us and believe in the power and the necessity of free speech,” Ms. Yaccarino said. “Sometimes in life and in business, standing for your values is the truly defining thing that makes leaders, and we’re going to hold on to that and keep pushing forward. No critic is ever going to deter us from our mission to keep fighting and protecting free speech.”

In the roughly 30-minute meeting, Ms. Yaccarino focused the blame on Media Matters and did not address Mr. Musk’s endorsement of the antisemitic post.

She also encouraged employees to be frugal during a period of decreased revenue caused by the advertiser pauses and think of ways the company could bring in more money.

“I would say be as fiscally responsible as possible,” the chief executive told her workers. “And that’s on a spectrum of critical-only and necessary travel to being a good steward of anything that might be related to an expenditure at the company.”

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