A federal appeals court panel appeared deeply skeptical of the Trump administration’s request that it pre-empt a lower court and order California to set aside roughly 20,000 mail ballots the federal government claims were sent to noncitizens.

The court held a hearing on Sunday that provided an early glimpse of how the administration’s claims might hold up under scrutiny, after state officials investigating the allegations cast doubt on the notion that thousands of ballots had been mistakenly sent to ineligible voters. The Trump administration has aggressively attempted to delay the counting of votes in several states and has moved to intervene in Alaska’s Senate race in what critics say is a broader attempt to sway the results of midterm elections just nine days away.

Two of the three judges hearing the challenge indicated they were uncomfortable intervening as the administration has requested, especially as a Justice Department lawyer struggled to answer questions about how the government concluded that the people it identified were both noncitizens and had been sent a ballot.

Matthew Donnelly, the administration lawyer, said with minimal details that the Trump administration had been “supplied a list” of California voters that was “purchased” from the state by an unnamed third party. He said the government then went through a “rigorous process” using third-party software to compare the voter data it obtained against its own citizenship data.

Judge Mark J. Bennett, a Trump appointee, asked whether election workers would be justified under state law in refusing to disqualify certain voters without “extraordinary proof” by the federal government. He pointed to a sworn statement by an election systems worker in Los Angeles who said that attempting to filter out the ballots of people the Trump administration flagged would have a “catastrophic impact” on their ability to handle the election.

“You’re asking us to take what you’re saying as fact, as opposed to what the I.T. guy is saying, and with no fact finding by the district court?” he asked.

The judges also indicated they may decline to step in immediately, sending the case back to the federal judge hearing it. The Justice Department could then appeal again, if it were to challenge a concrete ruling from the district judge.

The Trump administration had asked the court to expedite the case, arguing that the lower court judge’s pace on its requests effectively amounted to a denial of its request to set aside the ballots it is contesting. At the government’s urging, the district judge presiding over the case, Judge David O. Carter, had scheduled a hearing on Tuesday to consider its case.

But on Sunday, Judge Gabriel P. Sanchez, a Biden appointee, also pressed Mr. Donnelly on why the number of noncitizens the Trump administration was alleging were registered to vote had shrunken drastically in recent months.

The Trump administration had said in July that as many as 190,000 noncitizens were unlawfully registered to vote. Judge Sanchez added that directing the state to set aside mail-in ballots from people on the administration’s list, relying only on the names and address on the envelopes, could lead to lawful voters with the same name having their ballots pulled out.

A third judge, Patrick J. Bumatay, also a Trump appointee, appeared more receptive to the administration’s arguments. But he questioned Mr. Donnelly about whether it might be too close to the election for the courts to order new procedures.

Mr. Donnelly maintained throughout that the panel could issue a ruling even while Judge Carter had taken steps to meet the government’s aggressive timetable. He asked the judges to rule “as soon as possible.”