WASHINGTON — A federal judicial panel on Tuesday assigned the appeals court in Cincinnati to handle at least 34 lawsuits that have been filed around the country challenging the Biden administration’s attempt to mandate that large employers require their workers to get vaccinated against the coronavirus or submit to weekly testing.

A court clerk for the U.S. Judicial Panel on Multidistrict Litigation randomly selected the Court of Appeals for the Sixth Circuit by drawing from a drum containing entries for the twelve regional courts of appeal, each of which has at least one related case pending. The procedure can be used to consolidate cases that are all raising the same issue.

While simplifying the legal dispute, the step also had the effect of removing the matter from the Court of Appeals for the Fifth Circuit in New Orleans. This month, a three-judge panel there had blocked the government from moving forward with the rule — declaring that it “grossly exceeds” the authority of the occupational safety agency that issued it.

All three judges on that panel are conservatives, including two appointees of former President Donald J. Trump. It was not immediately clear which judges on the Sixth Circuit would be assigned to hear the matter, nor whether they would decide to carry forward with an injunction against the mandate or would instead let the government proceed for now amid briefings and arguments.

The Occupational Safety and Health Administration, a part of the Labor Department, issued the “emergency” standard this month. Under that rule, companies with at least 100 employees must require unvaccinated workers to wear masks indoors starting Dec. 5. Starting Jan. 4, any who remain unvaccinated must undergo weekly testing at work.

The rule makes an exception for employees who do not come into close contact with other people at their jobs — such as those who work at home or exclusively outdoors.

President Biden had instructed OSHA to develop the rule in September, when he also announced other vaccine mandates that rely on different legal authorities. Those include mandates for federal civilian employees, federal troops and workers for federal contractors.

A variety of plaintiffs — including several large employers and several Republican-controlled states — have filed lawsuits against the employer mandate, arguing that it was an unlawful overreach.

The cases generally argue that OSHA has no legitimate power to issue regulations protecting workers against exposure to disease, as opposed to workplace hazards like asbestos, and that framing the mandate as a workplace safety effort was a pretext for the Biden administration’s real motivation: pressuring Americans who have been reluctant to get vaccinated.

In earlier litigation before the Fifth Circuit, the Justice Department argued that the rule was necessary to protect workers from the pandemic and was well grounded in law.

Blocking the mandate “would likely cost dozens or even hundreds of lives per day, in addition to large numbers of hospitalizations, other serious health effects, and tremendous costs,” the Biden administration said in one such filing. “That is a confluence of harms of the highest order.”

The Fifth Circuit panel, however, sided with the plaintiffs, writing that in enacting the law that created OSHA and empowered it to issue “emergency” rules to protect workplace safety, Congress did not intend “to authorize a workplace safety administration in the deep recesses of the federal bureaucracy to make sweeping pronouncements on matters of public health affecting every member of society in the profoundest of ways.”

As a whole, the Sixth Circuit also tilts conservative. Of its 16 sitting judges, 5 were appointed by Democrats and 11 were appointed by Republicans. (However, one of the Republican appointees, Judge Helene N. White, was originally a nominee of a Democratic president, Bill Clinton, before being renominated by a Republican one, George W. Bush, as part of a political deal.)

The circuit also has 10 active “senior status” judges, meaning they are semiretired but still sometimes are assigned to panels; of those, two are Democratic appointees and eight are Republican appointees.

Whatever the Sixth Circuit does with the matter, the case appears destined to reach the Supreme Court for a definitive resolution.