The supreme court on Thursday blocked the Biden administration from enforcing a requirement that employees at large businesses be vaccinated against Covid-19 or undergo weekly testing and wear a mask on the job.

At the same time, the court is allowing the administration to proceed with a vaccine mandate for most healthcare workers in the US.

The court’s conservative majority concluded the administration overstepped its authority by seeking to impose the Occupational Safety and Health Administration’s (Osha) vaccine-or-test rule on US businesses with at least 100 employees. More than 80 million people would have been affected.

“Osha has never before imposed such a mandate. Nor has Congress. Indeed, although Congress has enacted significant legislation addressing the Covid-19 pandemic, it has declined to enact any measure similar to what Osha has promulgated here,” the conservatives wrote in an unsigned opinion.

In dissent, the court’s three liberals argued that it was the court that was overreaching by substituting its judgment for that of health experts. “Acting outside of its competence and without legal basis, the court displaces the judgments of the government officials given the responsibility to respond to workplace health emergencies,” Justices Stephen Breyer, Elena Kagan and Sonia Sotomayor wrote in a joint dissent.

When crafting the Osha rule, White House officials always anticipated legal challenges – and privately some harbored doubts that it could withstand them. The administration nonetheless still views the rule as a success at already driving millions of people to get vaccinated and for private businesses to implement their own requirements that are unaffected by the legal challenge.

Both rules had been challenged by Republican-led states. In addition, business groups attacked the Osha emergency regulation as too expensive and likely to cause workers to leave their jobs at a time when finding new employees already is difficult.

The vaccine mandate that the court will allow to be enforced nationwide covers virtually all healthcare workers in the country. It applies to healthcare providers that receive federal Medicare or Medicaid funding, potentially affecting 76,000 health care facilities as well as home health care providers. The rule has medical and religious exemptions.

Earlier on Thursday, Biden announced plans to send 1,000 military medical personnel to hospitals and medical facilities, the president said on Thursday, as he announced plans to purchase another 500m at-home Covid tests.

The military members will begin arriving in states across the country next week, amid a surge in cases largely attributed to the Omicron variant. This week a top government official admitted it was likely that most Americans would be infected with the coronavirus.

On Tuesday the US recorded a record number of hospitalisations due to Covid-19 as daily infections soared to more than 1.35m. A test kit shortage across the country continues to hamper efforts to control the Omicron variant, but a silver lining has emerged, with signs that Omicron may be peaking in parts of the north-east.

In New York City the number of new cases has flattened in recent days, the New York Times reported, while New Jersey and Maryland have seen a slight decrease in the number of infections.

“Every case is one too many, but if you watch the trend line, it looks like we may be cresting over that peak,” Kathy Hochul, governor of New York, said in a briefing this week.

“We are not at the end, but this is a glimmer of hope when we desperately need that.”

Speaking at the White House on Thursday, Biden said his administration would double its order of home test kits, which will be delivered free of charge to Americans, to 1bn.

The White House announced it would purchase 500m tests in December, but those tests are yet to be distributed.

“I know we’re all frustrated as we enter this new year,” Biden said, as he noted that virus cases have reached new heights. But he insisted that it remains “a pandemic of the unvaccinated”.

Biden said a website where people can request tests will launch next week. The president also announced that, for the first time, his administration was planning to make high-quality N95 masks, which are most effective at preventing transmission of the virus, available free.

The 1,000 members of the military will help mitigate staffing crunches at hospitals across the country, Biden said, with many facilities struggling because their workers are in at-home quarantines due to the virus at the same time as Covid-19 cases have surged.

They will supplement the more than 800 military personnel who have already been helping civilian hospitals since Thanksgiving, and the more than 14,000 national guard members who are assisting with testing and vaccinations.

This week Janet Woodcock, the acting head of the Food and Drug Administration, said most Americans were likely to contract coronavirus.

“I think it’s hard to process what’s actually happening right now, which is [that] most people are going to get Covid, all right?” Woodcock said.

Biden also announced that six additional military medical teams will be deployed to hospitals in Michigan, New Jersey, New Mexico, New York, Ohio and Rhode Island.

The US leads the world in the daily average number of new infections reported, accounting for one in every three infections reported worldwide, according to a Reuters tally.