WASHINGTON — Justice Sonia Sotomayor on Tuesday temporarily blocked the Obama administration from forcing some religious-affiliated groups to provide health insurance coverage of birth control or face penalties as part of the Affordable Care Act.

Acting at the request of an order of nuns in Colorado, Justice Sotomayor issued the stay just hours before the requirement was to go into effect on New Year’s Day. She gave the Obama administration until Friday to respond to the Supreme Court.

Justice Sotomayor’s order applies to the nuns, the Little Sisters of the Poor, and other Roman Catholic nonprofit groups that use the same health plan, known as the Christian Brothers Employee Benefit Trust. The groups’ lawsuit is one of many challenging the federal requirement for contraceptive coverage, but a decision on the merits of that case by the full Supreme Court could have broader implications.

“We are delighted with the ruling,” said Mark L. Rienzi, a lawyer at the Becket Fund for Religious Liberty, who represented the nuns in the lawsuit. “We are delighted that the Supreme Court will require the government to file briefs in the court on this matter.” The Little Sisters of the Poor operate nursing homes for low-income people in the United States and around the world.