A group of TikTok users has sued to overturn Montana's new statewide ban blocking the app, alleging that the law signed this week by Gov. Greg Gianforte violates the First Amendment.

The complaint filed Wednesday evening — hours after the governor's signature — compares TikTok to other types of media in claiming that the state lacks the authority to keep Montanans from accessing and creating lawful speech.

"Montana can no more ban its residents from viewing or posting to TikTok than it could ban the Wall Street Journal because of who owns it or the ideas it publishes," said the complaint, filed by five TikTok creators, including a small swimwear business, a rancher and a former Marine sergeant.

The lawsuit marks what may be the first challenge to a controversial ban that goes far beyond the restrictions Montana and other states have enacted to prohibit TikTok on official government devices.

In addition to the First Amendment claims, the lawsuit argues Montana's ban deprives TikTok users of many other rights without due process, in violation of the Fourteenth Amendment.

It also alleges the ban unconstitutionally conflicts with federal authority to set foreign policy and to oversee interstate commerce. And it claims the ban undercuts the federal government's powers under the International Emergency Economic Powers Act.

CNN is reaching out to Gianforte and Montana Attorney General Austin Knudsen for comment.