WASHINGTON — The Biden administration announced on Tuesday that it intends to appeal a Florida judge’s ruling that struck down a federal mask requirement on airplanes, trains, buses and other public transportation — but only if the Centers for Disease Control and Prevention decides that extending the measure is necessary.

The announcement from the Department of Justice came after a day of back and forth inside the White House, as administration officials faced a legal and political quandary: whether to let the judge’s ruling stand or to fight it, knowing that an appeal could result in a higher court, perhaps the Supreme Court, ruling against the administration and setting a lasting precedent that could undercut the C.D.C.’s authority.

In the end, the administration charted a careful course, publicly objecting to Monday’s ruling but putting off a final decision about whether to contest it. The Justice Department and the C.D.C. “disagree with the district court’s decision and will appeal, subject to C.D.C.’s conclusion that the order remains necessary for public health,” the department said in a statement.

“You are in the position of having two horrible choices,” said Lawrence O. Gostin, an expert in public health law at Georgetown University. “One choice is to risk forever taking away C.D.C.’s powers if this goes up to the 11th Circuit and ultimately the Supreme Court.

“And on the other hand,” he added, “if you let what I consider to be a lawless decision by this judge go forward, then C.D.C. is going to be gun-shy about doing things that it deems effective for the protection of the American public.”

The mask mandate — which also applied to transportation hubs like airports and train stations, and even to ride-sharing services like Uber — had been set to expire on May 3 even before the judge struck it down on Monday.

If the C.D.C. decides there is a public health basis for trying to reinstate and extend the mandate, the Justice Department will swiftly file an appeal. But if the C.D.C. decides otherwise, the administration will not appeal and the case will instead end as mooted — but without any signal of executive branch acquiescence to the judge’s view of its authority.

The Justice Department “continues to believe that the order requiring masking in the transportation corridor is a valid exercise of the authority Congress has given C.D.C. to protect the public health,” its statement said. “That is an important authority the department will continue to work to preserve.”

The C.D.C. imposed the mandate in early 2021, at the direction of the president. The agency had already extended it several times, most recently on April 13. At the time, it said it wanted to keep the requirement in place several more weeks while it assessed the potential severity of the Omicron subvariant known as BA.2, which recently became the dominant version among new U.S. cases.

As the administration considered its options on Tuesday, White House officials, including President Biden himself, were cautious in their public remarks. On a trip to New Hampshire to promote infrastructure spending, the president was asked by reporters whether people should wear masks on planes.

“That’s up to them,” Mr. Biden replied.

The Federal District Court judge in Tampa who struck down the mandate — Kathryn Kimball Mizelle — put forward a sharply constrained interpretation of the C.D.C.’s legal authority under the Public Health Service Act of 1944. If her view prevailed, the agency’s hands would be tied in future public health crises.

But a ruling by a district court judge is not a binding precedent. Appealing the matter would carry the risk that the court that oversees her — the Court of Appeals for the 11th Circuit in Atlanta — could issue a ruling that constrains the agency’s future conduct at least in its region, the Southeastern United States. A majority of the judges on that circuit are also Trump appointees.

And above it, the Supreme Court has a six-to-three conservative majority. In January, it blocked a Biden administration edict that large employers require workers to get vaccinated or submit to regular testing. (On the other hand, the court has permitted military officials to require service members and reservists to get vaccinated; it also upheld a federal mandate requiring health care workers at facilities receiving federal money to be vaccinated.)

Dr. Thomas Frieden, who directed the C.D.C. for eight years under President Barack Obama, noted that the C.D.C. has “very little regulatory authority” and said other pandemic-related actions — including a moratorium on evictions and the use of the border authority known as Title 42 to keep immigrants from seeking asylum — may have, in effect, reduced the agency’s political capital to keep the mask mandate in place.

“The broader question is, what is the appropriate use of mandates,” Dr. Frieden said. “The clearest case is for interstate travel, and so there is the risk that by pushing the envelope on other issues, we lost some of the narrative on what is an appropriate use of mandates.”

Some supporters of the mask mandate have viewed an appeal as risky.

“As tempting at it is to appeal it, because it’s a ridiculous ruling, the bigger issue is that you need to reserve the ability for the C.D.C. to act in case we have a big outbreak in the fall or the winter,” said Andrew Slavitt, a former senior health adviser to the president who helped run the administration’s Covid-19 response.

“Trump appointed 234 federal judges,” he added, “and if you end up there or in the Supreme Court, you could really damage your ability to respond to the pandemic in the future.”

But others spoke strongly in favor of an appeal.

“What worries me is the fact that this judge is saying that C.D.C. doesn’t have the authority to protect the health of people in America as they best see fit,” said Dr. Rich Besser, a former acting director of the C.D.C. He added that if the ruling stands, it would be “really damaging, because going into the next event you’ve got this ruling there and it hasn’t been contested.”

As a matter of politics, support for mask mandates has fallen in opinion polls as it has become clearer that healthy people who have been vaccinated and boosted — as well as those who remain unvaccinated but have survived a bout of Covid-19 — are generally at lower risk of experiencing severe or life-threatening symptoms if they get infected.

“The country clearly wants to move on,” said David Axelrod, a Democratic strategist who served as senior adviser to President Barack Obama. “Mandatory masking is a volatile issue. So my instinct is that the path of least resistance would be to stand down, on the grounds the clock is quickly running out anyway.”

But some people remain strongly in favor of such mandates. They have pointed to the continuing serious risk that any infection poses to immunocompromised people despite vaccination, and to the fact that very young children — while less likely to experience significant symptoms — are not eligible for vaccination.

Monday’s ruling took officials in the White House by surprise and frustrated them, two senior officials said. But on Tuesday, as travelers aboard airplanes took directions from pilots to unmask and riders aboard transit systems went mask-free, the Biden administration did not lay out a detailed plan to contest the ruling, even as public health experts warned that the C.D.C.’s authority to prevent the spread of a contagious virus was on the line.

Inside the C.D.C., officials felt their most recent extension of the mask mandate was reasonable, to give them time to assess the evidence and make a considered decision about whether to continue it.

“C.D.C. scientists had asked for 15 days to make a more data-driven durable decision,” Dr. Ashish K. Jha, the new White House coronavirus response coordinator, wrote on Twitter. “We should have given it to them. But I’ll continue to follow CDC guidance & mask up on planes.”

Katie Rogers contributed reporting.