In regard to state bans, the company said, “We believe the concerns driving these decisions are largely fueled by misinformation about our company.”

Both Indiana lawsuits alleged that TikTok is violating the state’s consumer-protection laws by deceiving the public about its operations. In the complaint focused on children, the state alleged the app is misrepresenting that it is appropriate for users ages 12 and older. For example, to have a 12-plus rating on Apple‘s App Store, TikTok must represent that references to mature themes, alcohol, drugs and sexual content are “infrequent/mild,” according to the lawsuit.

The state alleged that such material is abundantly available, from videos about hallucinogenic drugs and how to make alcohol taste like candy, to clips about strippers and sexual kinks, including bondage and rape fantasies.

South Dakota is already implementing a partial ban on the service. Last week, Gov. Kristi Noem, a Republican, issued an executive order banning TikTok from state agencies because of national-security concerns. The state tourism department has since deleted its TikTok account, which had 60,000 followers. South Dakota’s public broadcaster did the same. The state’s six public universities are evaluating next steps.

South Dakota was the second state to take such action. Nebraska did so in 2020, when TikTok was less popular than it is today.

On Monday, South Carolina Republican Gov. Henry McMaster said he requested that the state’s department of administration remove TikTok from government devices and block the site. The same day, lawmakers in Arkansas filed legislation for the coming 2023 session that would ban access to TikTok from state-owned or state-leased devices.

Maryland Gov. Larry Hogan, also a Republican, issued on Tuesday what he called an emergency cybersecurity directive to prohibit the use of certain Chinese and Russian developed technology, including TikTok, in the state’s executive branch.

TikTok is accused of violating Indiana’s state consumer-protection laws by misrepresenting that its video-sharing platform is appropriate for users 12 and up.Photo: Jessica Pons for The Wall Street Journal

These measures stop short of prohibiting all citizens from using the app. State employees in these cases can still use TikTok on personal devices. But the state-level actions mirror growing bipartisan worries in Washington, D.C., where lawmakers are debating a national ban.

Leaders from both parties have ratcheted up concerns about the Chinese government’s potential to order TikTok to collect data on American users, and to influence public discourse by controlling what people watch on the app. TikTok has said it has never received such requests and wouldn’t comply if asked.

Former President Donald Trump during his administration threatened to ban TikTok if it wasn’t brought under U.S. ownership. President Biden dropped that after the action was successfully challenged in court. The Biden administration is now negotiating with TikTok over a deal aimed at alleviating national-security concerns.

Meanwhile, Sen. Marco Rubio (R., Fla.) and other Republicans in Washington have come out publicly in support of a countrywide ban. Sen. Mark Warner (D., Va.) may support a ban too, but hasn’t decided, his spokeswoman said. Several leading lawmakers are threatening hearings over the matter in the Republican-held House next year.

In South Dakota, the ban has sown confusion and consternation. Some state employees say it is unclear if they can run state-affiliated TikTok accounts from personal devices.

The order bans the use of TikTok on “state-owned or state-leased equipment,” specifically prohibiting the app from being downloaded on such devices. It is less clear if the ban includes being able to access TikTok on personal phones through internet providers used in public spaces such as state-funded universities.

Ms. Noem didn’t respond to a request for comment. In issuing the executive order last Tuesday, she said the state had the duty to protect the private data of its citizens and hoped that other states would follow its lead.

The University of South Dakota’s TikTok account has about 24,000 followers, more than double its student population. A social-media analytics company, RivalIQ, ranked USD’s TikTok account as the second most-engaging university-run TikTok presence, behind No. 1 Central Michigan University. RivalIQ said USD stood out for engaging with students and creating whimsical moments around campus.

The South Dakota order inspired Rep. Mike Gallagher (R., Wis.) to ask Wisconsin Gov. Tony Evers to ban TikTok from the state’s government devices, Mr. Gallagher’s spokesman said. In a letter sent Tuesday and signed by other Wisconsin Republican congressmen, Mr. Gallagher urged the Democratic governor to delete his TikTok account, which he has used for campaigning.

Arkansas lawmakers drafted a bill on Monday for the 2023 legislative session to ban TikTok. And while the state’s GOP Gov. Asa Hutchinson hasn’t made any moves to ban the app, Governor-elect Sarah Huckabee Sanders, also a Republican, said she would work to address what she called the predatory actions of China.

“Everything is on the table,” she said. “Including going after TikTok.”