WASHINGTON — Supreme Court Justice Sonia Sotomayor granted a temporary exemption late Tuesday to a small group of Catholic nuns that shields it from having to comply with a part of President Obama's healthcare law that requires it to provide contraceptive coverage in its insurance plans.

She acted on an emergency appeal from lawyers for the group who said the nuns faced "draconian fines" beginning on New Year's Day if they failed to comply with the law widely known as Obamacare.

Sotomayor gave the government until Friday to file a response in the case. Her order extends only to the group of nuns and does not apply more broadly to the Affordable Care Act and its requirements.

The Supreme Court is facing a series of appeals from religious organizations and private corporations whose owners object to paying for contraceptives. In March, the court will hear two cases involving corporations and the contraceptive mandate.

The Obama administration has exempted churches and other religious groups from providing contraceptive coverage. However, it has granted a more limited exemption for religiously affiliated charities. Although they need not pay for this coverage directly, their insurers are required to include the coverage in their policies.

Nonetheless, several religious charities have continued to press for exemptions to the law. And on Tuesday evening, hours before the mandate was to take effect, they sent several emergency appeals to the court seeking an emergency exemption.

It was unclear how the Obama administration would proceed after Sotomayor's order. Obama is vacationing with his family in Hawaii this week, and the White House is not expected to make any comment before the Justice Department files a response to Sotomayor's ruling on Friday.

A number of religious groups with similar objections have vigorously challenged the Affordable Care Act in court. The Colorado order of nuns, the Little Sisters of the Poor, asked for the last-minute ruling Tuesday because the healthcare law's provisions go into effect Jan. 1.

In late November, the Supreme Court agreed to hear several cases that could settle the dispute between the Obama administration and businesses run by Christian conservatives over whether those companies must pay for birth control if providing that coverage is in conflict with the religious beliefs of the business owner.

The November announcement that the Supreme Court would hear the constitutional challenge to the birth control mandate in Sebelius vs. Hobby Lobby Stores Inc., as well as another case, signaled a new phase of the political battle over the healthcare law.

David Green, founder of Oklahoma-based Hobby Lobby Stores, has argued that business owners "should not have to choose between violating their beliefs and violating the law."

david.savage@latimes.com

maeve.reston@latimes.com

Savage reported from Washington and Reston from Honolulu.