WASHINGTON — The Supreme Court on Wednesday temporarily allowed the Trump administration to enforce restrictions on the nation’s refugee program, but it let stand a court order from Hawaii that grandparents and other relatives who want to travel to the United States to visit family must be admitted while the case proceeds on appeal.

The justices, in a brief order, rejected the administration’s request that it clarify the scope of their decision last month temporarily reinstating the ban but allowing people with “a credible claim of a bona fide relationship with a person or entity in the United States” to enter the country. The court said the United States Court of Appeals for the Ninth Circuit, in San Francisco, should address the question.

Justices Clarence Thomas, Samuel A. Alito Jr. and Neil M. Gorsuch said they would have blocked the Federal District Court in Hawaii entire order while the case proceeds, including the part that allowed grandparents and other relatives of United States residents to travel from six mostly Muslim countries.

The administration has read the Supreme Court’s decision last month narrowly, excluding many travelers from six mostly Muslim countries with family members in the United States, as well as many refugees.

Later that day, the administration filed a motion asking the Supreme Court to clarify its decision.

The Supreme Court’s decision last month did not specify who qualified as a close relative, though it did say that spouses and mothers-in-law “clearly” counted.

The State Department, in interpreting the ruling, said that parents, children, spouses, parents-in-law, sons- and daughters-in-law, fiancés and siblings of those already in the United States would be included. Close relations would not include grandparents, grandchildren, uncles, aunts, nephews, nieces, cousins, and brothers- and sisters-in-law.

The department said it drew on guidelines set out in some provisions of the immigration laws. Judge Watson responded that other provisions are more expansive, and include grandparents, grandchildren, aunts, uncles, brothers-in-law and sisters-in law.

The administration also excluded refugees whom resettlement agencies had planned to assist in moving to the United States. Judge Watson disagreed, writing that the Supreme Court had meant to allow such people to enter the country.

Judge Watson’s order, the brief said, did nothing to stop the administration from enforcing its travel ban “against more than 85 percent of refugees, or to exclude countless extended family members — second cousins, great-aunts, and so forth — and other individuals who indisputably lack close relationships with American individuals and entities.”

Challenges to Mr. Trump’s travel bans have been ricocheting around the federal courts for almost as long as he has been president.

His first ban, issued in January, caused chaos at the nation’s airports until it was blocked by the courts. Rather than appealing to the Supreme Court, the administration issued a revised executive order in March. But that order, too, was blocked by federal appeals courts, which ruled that it violated the Constitution by discriminating based on religion and that it exceeded Mr. Trump’s statutory authority.

In June, the Supreme Court agreed to hear appeals from those decisions, scheduling arguments for October.