WASHINGTON — The White House authorization of one more bombing campaign in Afghanistan, just weeks before the U.S. military mission is set to end, has a modest stated goal — to buy time for Afghan security forces to marshal some kind of defense around the major cities that are under siege by a surging Taliban.

But the dozens of airstrikes, which began two weeks ago as the Taliban pushed their front lines deep into urban areas, also laid bare the big question now facing President Biden and the Pentagon as the United States seeks to wind down its longest war. Will the American air campaign continue after Aug. 31, the date the president has said would be the end of combat involvement in Afghanistan?

The White House and the Pentagon insist these are truly the final days of American combat support, after the withdrawal of most troops this summer after 20 years of war. Beginning next month, the president has said, the United States will engage militarily in Afghanistan only for counterterrorism reasons, to prevent the country from becoming a launchpad for attacks against the West. That would give Afghan security forces mere weeks to fix years of poor leadership and institutional failures, and rally their forces to defend what territory they still control.

Pentagon and White House officials say the current air campaign can blunt the Taliban’s momentum by destroying some of their artillery and other equipment, and lift the sagging morale of Afghan security forces.

But administration officials say the Pentagon will most likely request authorization from the president for another air campaign in the next months, should Kandahar or Kabul, the capital, appear on the verge of falling. Mr. Biden appeared to hold out that possibility last month when he said that the United States had “worked out an over-the-horizon capacity that can be value added” if Kabul came under serious threat, phrasing the military often uses to suggest possible airstrikes.

Such a move would foreshadow the inching toward a longer campaign that could give Mr. Biden space between his decision to withdraw American troops and an eventual fall of Kabul, and the possible specter of evacuations of the U.S. and other Western embassies, like the scene that preceded the fall of Saigon in 1975, when Americans were evacuated from a rooftop by helicopter.

Mr. Biden’s aides say that he is aware of the risks, but that he remains skeptical of any effort by the Pentagon that looks as though it is prolonging the American military engagement. Still, officials say that they expect Defense Secretary Lloyd J. Austin III and Gen. Mark A. Milley, the chairman of the Joint Chiefs of Staff, to approach Mr. Biden at the end of August about the possibility of continuing airstrikes into September if the Taliban look as if they are about to overrun key population centers.

Already, the Taliban have been making advances, sweeping through the Afghan countryside and closing in on the center of Kandahar. Taliban fighters launched rockets over the weekend at the airport in Kandahar, and fierce fighting near Herat shut down the airport there.

At the moment, the official line from the White House and the Pentagon is that these are truly the final days of American combat support.

“My personal belief is that the closer the Taliban get to the urban areas, I think the fighting gets more intense, and they can’t take advantage like they could in the rural areas,” said Gen. Joseph L. Votel, the former commander of United States Central Command. “As they get to the built-up areas, where there’s leadership in place who will be fighting for their lives, I think those fights will become more difficult.”

But that has not been the case in recent days and weeks, as Taliban fighters have entered several provincial capitals such as Kunduz in the north, Kandahar and Lashkar Gah in the south and Herat in the west.

Even with American B-52 bombers and AC-130 gunships helping where they can, the Taliban have pushed into Lashkar Gah, the capital of Helmand Province.

One Afghan officer in the city described the situation last week as “hell.” Even now, with reinforcements and continued American airstrikes — there were at least two on Monday morning — fighting was still continuing in nearly every part of the city.

But helping Afghan partners fight for their lives is the point of the stepped-up bombing campaign, military officials said.

Mohammad Sadiq Essa, a spokesman for the Afghan Army corps fighting in Kandahar, said the U.S. strikes had been useful in “busting the momentum of the Taliban.” But continued strikes from both U.S. and Afghan aircraft, especially around urban areas, run the risk of causing a high number of civilian casualties.

Since the U.S. military began its official withdrawal in May, thousands of civilians have been killed or wounded — the highest number recorded for the May-to-June period since the United Nations began monitoring these casualties in 2009.

Mr. Biden, in announcing the withdrawal of U.S. troops, initially gave Sept. 11 as the date when the American combat mission was to end. Then last month, he said it would wrap up by Aug. 31. That gave the Pentagon — and Afghan forces — just over a month to slow the Taliban surge.

“We’re prepared to continue this heightened level of support in the coming weeks if the Taliban continue their attacks,” Gen. Kenneth F. McKenzie Jr., the top American general overseeing operations in Afghanistan, said last week in explaining the intensified airstrikes.

What is happening now echoes the past. After the end of the U.S. combat mission in Afghanistan in 2014, the Obama administration had to backtrack and permit more airstrikes for the Afghan security forces as they lost the bases and outposts that international forces had transferred to them.

In the past, air power has not been enough unless it was accompanied by a competent force on the ground. Right now, those forces are still lacking, with the Afghan military relying on an exhausted commando corps to fill in for many police officers who have fled or surrendered and army troops who refuse to fight or even venture outside their bases.

Administration and military officials have voiced conflicting views on whether the United States will continue airstrikes after Aug. 31 to prevent Afghan cities and the Afghan government, led by President Ashraf Ghani, from falling. General McKenzie declined last week to say that U.S. airstrikes would end at the end of the month.

Mr. Biden has been clear in meetings with his senior aides and advisers that continued American bombing runs from the skies over Afghanistan after the pullout are not what he wants, administration officials said. But his hand might be forced if Taliban forces are on the verge of overrunning Kandahar or even Kabul, where the United States maintains an embassy, with some 4,000 people.

The Afghan military is trying to hold key cities and roads, a strategy that American military officers have pushed for years while the Afghan security forces, backed by U.S. air power, clung to far-flung, isolated and indefensible districts after the U.S. combat mission ended in 2014. Afghan officials largely ignored the suggestions until now, unwilling to cede any territory — despite its strategic insignificance — to the insurgents.

So for the time being, the United States is trying to make the fight as difficult as it can for the Taliban. “This is about buying time,” General Votel said in an interview. “It’s about blunting and slowing down the Taliban and helping the Afghans to get a little more organized.”

Defense Department officials said they expected the strikes, up to five a day, to continue at least through August. The attacks, carried out by armed Reaper drones and AC-130 aerial gunships, are targeting specific Taliban equipment, including heavy artillery, that could be used to threaten population centers, foreign embassies, Afghan government buildings or compounds, or airports, officials said.

A Taliban official shrugged off the presence of hulking B-52 bombers that have appeared in Afghanistan’s skies, though officially the group has decried the bombings as a breach of the 2020 peace agreement with the United States and promised consequences.

The American airstrikes have underscored the shortcomings of the Afghan Air Force, which U.S. officials say is overstretched and breaking down.

“All of the Afghan Air Force’s aircraft platforms are overtaxed due to increased requests for close air support, intelligence, surveillance, reconnaissance missions and aerial resupply now that the ANDSF largely lacks U.S. air support,” the special inspector general for Afghanistan reconstruction said in a report released last week, referring to Afghan security forces.

The departure of all but a couple of hundred U.S. aircraft maintenance contractors has led to sharp decreases in readiness rates for five of the seven aircraft in the Afghan air fleet, the report found. But even with the litany of issues, including the loss of aircraft to Taliban fire at an increasing rate, Afghan pilots have been trying to support the forces.

Helene Cooper and Eric Schmitt reported from Washington, and Thomas Gibbons-Neff from Kabul, Afghanistan. Taimoor Shah contributed reporting from Kandahar, Afghanistan.