The Supreme Court on Tuesday denied Florida Gov. Ron DeSantis' appeal to lift a lower court order preventing the state from enforcing a new law that bans bars from "knowingly" hosting drag queen performances with minors in the audience.

At issue is a lawsuit challenging a Florida law passed in April that prevents children from exposure to sexually explicit "adult live performances" at restaurants and bars and mandates that establishments that allow such performances with minors in the audience could get alcohol or operating licenses revoked.

Hamburger Mary's, a restaurant and bar in Orlando, argued the law was written so broadly as to have a "chilling effect" on free-speech rights.

A district judge agreed, finding the plaintiff was likely to succeed at trial on First Amendment grounds and granted a preliminary injunction to stop the law from taking effect while the case moves through the courts.

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The Supreme Court building

The U.S. Supreme Court (AP Photo / J. Scott Applewhite / File)

The DeSantis administration appealed to the Supreme Court, asking the justices to stay that order and arguing it improperly applied to other places of business in Florida that aren't party to the suit.

But the Supreme Court on Thursday denied that request.

In an order written by Justice Brett Kavanaugh, the court said that while the case centers around First Amendment questions, the state's appeal "challenges only the scope of relief ordered by the District Court — namely, that the injunction prohibits state enforcement of the law not only against Hamburger Mary’s but also against other entities that are non-parties to this litigation."

"To begin with, although Florida strongly disagrees with the District Court’s First Amendment analysis, Florida’s stay application to this Court does not raise that First Amendment issue," the order says.

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Supreme Court justices

The justices of the U.S. Supreme Court (Olivier Douliery / AFP via Getty Images / File)

"Therefore, the Court’s denial of the stay indicates nothing about our view on whether Florida’s new law violates the First Amendment," it reads.

"The question of whether a district court, after holding that a law violates the Constitution, may nonetheless enjoin the government from enforcing that law against non-parties to the litigation is an important question that could warrant our review in the future," Kavanaugh wrote.

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Ron DeSantis

Ron DeSantis (Sergio Flores / AFP via Getty Images / File)

"But the issue arises here in the context of a First Amendment overbreadth challenge, which presents its own doctrinal complexities about the scope of relief. This case is therefore an imperfect vehicle for considering the general question of whether a district court may enjoin a government from enforcing a law against non-parties to the litigation. For that reason, the Court is not likely to grant certiorari on that issue in this particular case," he continued. 

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"In sum, because this Court is not likely to grant certiorari on the only issue presented in Florida’s stay application, it is appropriate for the Court to deny the application," Kavanaugh concluded.

The Associated Press contributed to this report.