State attorneys general are emerging as a new regulatory threat to the U.S. companies that dominate the internet.

State officials are raising risks for companies such as Facebook Inc., Twitter Inc. and Alphabet Inc.’s Google as the states begin piecing together a coordinated legal strategy for confronting the firms over alleged antitrust violations and data-privacy abuses, and over what some Republicans say is a suppression of conservative speech.

Tensions have been simmering for months, but they surfaced publicly last week when the Justice Department said U.S. Attorney General Jeff Sessions would meet with several state attorneys general later this month to discuss a “growing concern” that the companies are hurting competition and “stifling the free exchange of ideas” on their platforms.

The announcement—released amid last week’s congressional hearings into the practices of Facebook and Twitter—shed little light on who was raising the concerns or what remedies might be under consideration. But recent comments by several of the state attorneys general suggest they are actively exploring an antitrust investigation and hope to enlist Washington.

“I think the companies are too big, and they need to be broken up,” Republican Louisiana Attorney General Jeff Landry said Thursday in a radio interview.

Twenty years ago, Microsoft Corp. faced lengthy antitrust litigation brought by about 20 state attorneys general, along with the Justice Department. So far, the current generation of internet giants have largely avoided antitrust enforcement action in the U.S., even as the European Union has imposed multibillion-dollar fines on Google for alleged abuses involving its search function and Android mobile-phone system.

And yet, the U.S. regulatory environment is growing considerably less friendly to tech. Several Trump administration agencies, including the Federal Trade Commission, are examining the industry, and Mr. Trump himself recently railed against the internet giants and has attacked behemoths like Amazon.com Inc. and Google..

Last week, lawmakers in Washington held the latest in a series of hearings this year into a range of tech issues, including alleged Russian hacking, privacy and user data and criminal activity. A persistent theme was the question of regulating big tech.

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The Justice Department declined to comment beyond last week’s announcement. It isn’t clear how seriously the DOJ is taking the calls for action by the states, or whether the department’s division responsible for antitrust enforcement had any role in planning Mr. Sessions’ meeting.

The Justice Department’s antitrust chief, Makan Delrahim, has been holding workshops to explore cutting-edge competition issues. He has given several speeches discussing competition in the digital space and laying out potential frameworks for any antitrust challenges.

The FTC is to begin a series of hearings this week to consider competition concerns in the internet economy, among other issues.

A spokesman for Twitter declined to comment, while Google didn’t respond to requests for comment. A spokesman for Facebook pointed to comments by CEO Mark Zuckerberg, who said he is open to regulation that protects the privacy of users. He didn’t comment on the prospect of an antitrust action or anything specific to the state officials.

Republicans’ allegations that the tech companies suppress conservative voices has bubbled up for months in conservative media and was amplified by Mr. Trump late last month. Democrats have said that is the issue—more than antitrust policy—behind the coming Justice Department meeting, with Republicans hoping to stir their conservative base ahead of November elections

All the attorneys general who are expected to attend this month’s meeting in Washington are Republicans, with Democratic officials saying they have yet to be invited.

Texas Republican Attorney General Ken Paxton also said Friday he would be attending. “We must work together to ensure that online economic competition operates fairly and transparently, so that Americans across the political spectrum can make informed choices and the public discourse can flourish,” his communications director, Marc Rylander, said in a statement. The attorney general of Missouri, Republican Josh Hawley, now running for a U.S. Senate seat, has already begun an antitrust investigation into Google.

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Some Democratic attorneys general, for their part, have raised antitrust worries about the firms. “Maybe it’s a century ago with the trust busters, where abuses were taken by the railroads and the barons of industry,” Rhode Island Attorney General Peter Kilmartin saying in June. “Maybe we’re waiting for a Teddy Roosevelt to come in.”

The Republican Mr. Landry—current president of the National Association of Attorneys General—said he believes the competition problems created by the giant companies likely will have to be solved through antitrust litigation.

“In my opinion you’re not going to fix this legislatively,” Mr. Landry, a Republican former congressman, said on Shreveport radio station KEEL. “You’re going to have to fix this like we’ve always fixed monopolies in this country; you’re going to have to take an antitrust suit.”

The tech companies adamantly deny they have sought to suppress conservative content on the internet. And even some big tech critics say they hope the legal concerns about the social-media platforms aren’t being weaponized for political gain.

“We obviously think there are competition problems,” said Matt Stoller, a fellow at the Open Markets Institute, a think tank that has criticized the internet platforms. But the current focus on the treatment of conservative viewpoints could suggest “an attempt to use legitimate concerns to organize legal power for one party and point of view, and that’s dangerous,” he added.

Experts have raised a range of doubts over whether an antitrust probe into the platforms could fly. Those include the federal immunity law that has frustrated many state investigations into the internet platforms’ practices. Some believe, however, the allegations of free-speech suppression could help undermine the platforms’ immunity claims.

—Brent Kendall contributed to this article.

Write to John D. McKinnon at john.mckinnon@wsj.com and Douglas MacMillan at douglas.macmillan@wsj.com