In the latest arguments over President Donald Trump’s travel ban, a three-judge panel of a federal appeals court in Seattle indicated Monday that it would continue allowing grandparents and other relatives of U.S. residents to travel here from six predominantly Muslim countries.

But the judges were less forthcoming about their views on exceptions to a second part of the ban, suspending the nation’s refugee program.

In July in a provisional ruling, one that will last only until the appeals court rules, the Supreme Court allowed exceptions to the ban for many relatives but not for most refugees. The Supreme Court will hear arguments in the case in October. The appeals court is set to decide what will happen while the justices consider the case.

By the end of Monday’s 40-minute argument, it seemed clear that the appeals court, the 9th U.S. Circuit Court of Appeals, would rule that the administration had overreached, at least as far as relatives were concerned.

“How can the government take the position that a grandmother or grandfather or aunt or uncles of a child in the United States does not have a close familial relationship?” Judge Ronald M. Gould asked. “Like what universe does that come from?”

How the appeals court would deal with refugees was less clear.

Hashim M. Mooppan, a Justice Department lawyer, argued that an agreement by a resettlement agency to care for a refugee was insufficient to allow entry. Colleen Roh Sinzdak, a lawyer representing Hawaii, which is challenging the ban, said such an agreement satisfied the criteria set out by the Supreme Court.

The travel ban, issued in January and revised in March, caused chaos at airports nationwide. It has also prompted a cascade of litigation.

In June the Supreme Court agreed to decide whether the revised version of the ban was lawful, and it has scheduled arguments for Oct. 10.

Two federal appeals courts had blocked central parts of the ban. One said it violated the Constitution because it discriminated based on religion; the other said that it exceeded the president’s statutory authority to control immigration.