WASHINGTON — Military commanders are seeking to deploy an aircraft carrier specifically to help protect NATO troops in Afghanistan as they withdraw, the clearest sign yet that the Pentagon is preparing for a fight as it closes the books on America’s longest war.

But the deployment — likely to fall on either the overstretched Eisenhower or the Theodore Roosevelt, the carrier at the center of a coronavirus crisis last year — will mean an additional load on the Navy’s exhausted warships and crews, after a rash of extended deployments over the past few years.

The request, from Gen. Kenneth F. McKenzie Jr., the head of Central Command, is en route to the desk of Defense Secretary Lloyd J. Austin III, military officials said. Mr. Austin is expected to decide soon.

The appeal is part of a withdrawal that the Pentagon describes as a “military retrograde operation.” Such movements often require — as they do now — sending additional troops and equipment to make sure departing forces can leave safely.

“It’s not over yet,” Gen. Mark A. Milley, the chairman of the Joint Chiefs of Staff, told reporters aboard his airplane last week, just after President Biden announced the Afghanistan withdrawal. “We have a lot of work ahead of us to make sure we get out in a good and orderly fashion, protect the force and continue defending America.”

The Pentagon is concerned that the exit could draw fire from Taliban fighters hoping to put a final punctuation on what the militant group is presenting as a humiliating American defeat. Biden administration officials have sounded a tough line about retaliation if the Taliban mounts any attacks on retreating troops. But the insurgent group’s intentions are unclear while its leadership meets in Pakistan to decide its next step.

To back up their warning, Defense Department officials say they will need fighter squadrons operating from carriers in the region and a slew of other warplanes, operating around the clock, to give cover to troops as they depart Afghanistan. Flights from carriers in the Persian Gulf are costly, and take repeated refueling trips just for the aircraft to stay over Afghanistan for a relatively short period.

“We’re going to protect the force,” General Milley said. “We have a change of mission. Our mission is to conduct a retrograde while protecting the force, and that’s exactly what we’re going to do.”

General McKenzie’s request, military officials said, asks for 24-hour support from a carrier, with its attendant fighter squadrons, and is being viewed as a specific reference to the Eisenhower, which left its home port in Virginia in February and headed to the Mediterranean Sea. There, it took part in exercises with Italian and Moroccan naval forces. The Eisenhower is now in the Arabian Sea.

Capt. Bill Urban, a spokesman for Central Command, declined to comment. The Pentagon press secretary, John F. Kirby, said on Wednesday that Mr. Austin “has made clear that we will execute the drawdown in Afghanistan in a safe, orderly and deliberate manner, and that we will do everything possible to protect our troops in the process.”

He, too, declined to discuss the request, saying that “for operational security reasons, we will also not preview specific force protection measures being planned.”

Current and former senior Navy officials said immediate military missions may demand that warships’ deployments be extended. But when this repeatedly happens, the long-term health and readiness of the fleet can erode, jeopardizing the Navy’s ability to meet future missions.

“We have these national assets like aircraft carriers to be available in times of crisis, especially when they’re needed to protect the lives of troops on the ground,” Vice Adm. Kevin Donegan, a retired Fifth Fleet commander, said in an interview. “But you don’t want this to be a routine thing, and that’s what’s happened in the past.”

Aboard the Eisenhower, some sailors were already worried about their deployments being extended, particularly if the carrier ends up providing air operations throughout the American withdrawal from Afghanistan, which Mr. Biden said must be completed by Sept. 11.

A Defense Department official said this week that it remained an open question whether American troops would have to fight their way out of Afghanistan or whether the withdrawal would be peaceful. He spoke on the condition of anonymity to speak publicly about the matter.

In recent years, aircraft carriers, which act as sovereign American territory at sea, have increasingly been used for flexing military power against adversaries.

For example, in January, the Pentagon reversed itself and ordered the aircraft carrier Nimitz to remain in the Middle East because of Iranian threats against President Donald J. Trump and other American officials, just three days after ordering the warship home as a signal to de-escalate rising tensions with Tehran.

The acting secretary of defense at the time, Christopher C. Miller, abruptly reversed his previous order to redeploy the Nimitz, which he had done over the objections of his top military advisers. The military had for weeks been engaged in a show-of-force strategy to deter Iran from attacking American personnel in the Persian Gulf.

In the end, the nuclear-powered warship did not return home until late February, some 10 months after it departed its home port in Bremerton, Wash. The sailors, pilots and crew aboard had witnessed an unfolding pandemic, a contested presidential election, a riot at the Capitol, and civil protests around the death of George Floyd, all while at sea.

Now, lawmakers are raising questions about the extended carrier deployments in recent years. In a letter this month to Mr. Austin and the deputy defense secretary, Kathleen Hicks, members of the House Armed Services Committee cited the “need for increased prudence and scrutiny” when it comes to requests for deployments. The lawmakers spoke of services “scrambling at a time when they need to rebuild the health of the force.”

“At this rate, the desire to solve every immediate problem regardless of its strategic prioritization, may hollow the force for the next generation,” the letter said.

Helene Cooper and Eric Schmitt reported from Washington, and Thomas Gibbons-Neff from Kabul, Afghanistan.