WASHINGTON — In temporarily blocking enforcement of the part of President Obama's health care law that requires many employers to provide health insurance coverage for birth control or face penalties, Justice Sonia Sotomayor on Tuesday opened a second front in Supreme Court challenges to the provision.

The initial front opened in November, when the justices agreed to hear a pair of cases from for-profit companies challenging that provision. Now Justice Sotomayor has ordered the Obama administration to file a brief by Friday morning responding to a different kind of challenge, this one from groups affiliated with religious organizations.

In the meantime, she issued a temporary injunction barring the administration from enforcing the birth control requirement against an order of Colorado nuns, the Little Sisters of the Poor, and related groups.

After the brief is filed, Justice Sotomayor or the full court could extend or dissolve Tuesday's temporary injunction while litigation moves forward in the lower courts. It is also possible that the Supreme Court would agree to hear the case immediately.

To understand the context of Justice Sotomayor's decision, it helps to look at the details of the Affordable Care Act. The law distinguishes among three kinds of organizations: religious employers, for-profit corporations and nonprofit groups affiliated with religious organizations but not owned or controlled by them.

Under the law, religious employers like churches are exempt from the contraceptive requirement. For-profit corporations fall on the other end of the spectrum and are not exempt. Nonprofit groups affiliated with, but not owned or controlled by religious organizations, like the Little Sisters of the Poor, fall in the middle. Although such groups need not provide coverage themselves, they must sign a certification allowing insurance companies to do so.

The dispute in the new case is whether that certification itself amounts to conduct that violates the groups' religious faith.

In their Supreme Court brief, the nuns said they faced ruinous fines if they failed to comply. They calculated that they would have to pay "an annual fine of approximately $2.5 million — for an organization that cares for 69 elderly poor people and operates with an annual budget of approximately $6 million."

According to the Becket Fund for Religious Liberty, which represents the nuns and other challengers to the requirement, preliminary injunctions had been granted in the lower courts in 18 of 20 similar cases. Justice Sotomayor acted after the United States Court of Appeals for the 10th Circuit, in Denver, declined to issue an injunction.

Mark Rienzi, a lawyer with the Becket Fund, said he welcomed the development. "The government has lots of ways to deliver contraceptives to people," he said. "It doesn't need to force nuns to participate."

In a separate case, a divided three-judge panel of the United States Court of Appeals for the District of Columbia Circuit on Tuesday issued its own injunction against the requirement. But in a dissent, Judge David S. Tatel wrote that the certification requirement aided rather than hindered religious liberty.

"Simply put," he wrote, "far from imposing a 'substantial burden' on appellants' religious freedom, the challenged provision allows appellants to avoid having to do something that would substantially burden their religious freedom."

The challenges to the health care law from for-profit corporations involve slightly different legal questions. One of them is whether such corporations are "persons" for purposes of the relevant federal law, the Religious Freedom Restoration Act of 1993. The question of whether corporations have religious liberty rights is reminiscent of the Supreme Court's determination in Citizens United and other decisions that corporations have free speech rights.

The for-profit corporations challenging the contraception coverage requirement say it requires them to choose among three unpalatable options. They can pay for insurance coverage that their owners say they find objectionable; they can pay penalties for failing to do so; or they can drop coverage entirely and pay a different penalty for doing that.

The Justice Department has said that for-profit companies are unprotected by the religious freedom law, and that the contraception coverage requirement does not impose a substantial burden on them in any event.

When the Supreme Court agreed to hear the cases in November, Jay Carney, the White House press secretary, said important public health interests were at stake.

"Our policy is designed to ensure that health care decisions are made between a woman and her doctor," he said. "The president believes that no one, including the government or for-profit corporations, should be able to dictate those decisions to women."

The two cases concerning for-profit corporations, Sebelius v. Hobby Lobby Stores, No. 13-354, and Conestoga Wood Specialties v. Sebelius, No. 13-356, are likely to be argued in March and decided by June.

That will be two years after a closely divided Supreme Court upheld the part of the law that required most Americans to obtain health insurance or pay a penalty.