By contrast, Russian forces are firing about 60,000 artillery shells and rockets each day in the Donbas fighting, according to a senior adviser to the Ukrainian military command who was not authorized to speak publicly.

Michael Kofman, the director of Russia studies at CNA, a research institute in Arlington, Va., said ammunition supplies would be critical to the final outcome in the battle for eastern Ukraine.

“This war is far more about attrition by artillery than maneuver, which means one of the deciding factors is who has more ammunition,” he said.

That Ukraine was running low on ammunition has hardly been a secret. Ukrainian officials flagged the problem months ago. On the front lines, commanders watched, alarmed, as stocks dwindled mid-battle. Soldiers say requests for artillery support go unanswered, for lack of shells.

Vadym Mischuk, 32, a Ukrainian soldier who had just rotated off the frontline near the eastern city of Bakhmut, said Thursday that there is so much Russian artillery fire that “we don’t even hear ours.” One soldier, who declined to provide his name for security reasons, estimated that for every one Ukrainian shell fired, the Russians fired 10.

The Ukrainian military has been honest about the shortfalls — something an army would not typically telegraph to the enemy in a war — perhaps because doing so adds a sense of urgency to appeals for more powerful Western weaponry.

“In early March we were already well aware that during intensive war with Russia our resources were depleting,” Ukraine’s defense minister, Oleksiy Reznikov, wrote on Facebook on Thursday. He added, “Relying solely on Soviet weapons was definitely a losing strategy.”

Even before the invasion, Ukraine’s ammunition depots had been targets for saboteurs, regularly blowing up like gigantic, lethally dangerous fireworks displays.

Spies or drones dropping incendiary devices were blamed in many cases. Between 2015 and 2019, six ammunition depots blew up in Ukraine, burning about 210,000 tons of ammo, or three times more than the Ukrainian army expended in the same time span fighting Russian-backed separatists, according to Radio Free Europe/Radio Liberty.

Following Russia’s invasion, NATO countries have stepped in to bolster Ukraine’s supply of ammunition, but the transfers have not always gone smoothly. Countries of the old Warsaw Pact and NATO countries used different calibers of ammunition — an enduring legacy that means much of Ukraine’s arsenal, built decades ago to Soviet specifications, cannot fire Western ammunition.

Ukraine’s newly acquired hoard of NATO’s 155-millimeter artillery shells is now larger than its entire artillery ammunition stockpile before the war started, Mr. Reznikov said. But the Ukrainian forces have too few guns at the front to fire the munitions, and are facing extensive logistics challenges not only to get them into the fight, but also to maintain them once there.

Some European countries have shipped so many of their own ammunition reserves to Ukraine — in some cases up to 30 percent — that they’re increasingly anxious about replenishing their stocks, European Union officials said.

Officials said that while there was still a relatively steady flow of military equipment from the E.U. and its allies, Ukraine was not receiving as much heavy artillery as it needs.

With artillery shells in short supply, Ukrainian forces have adjusted their tactics to compensate for the lack of artillery support. On Friday, for example, a tank unit in Donbas was using a Ukrainian T-64BV tank more like an artillery piece than a main battle tank.

Instead of attacking targets directly, the tank drove several kilometers toward the front, positioned itself in a tree line, and lobbed shells at Russian positions while a Ukrainian officer adjusted its aim over the radio and using a drone overhead — the procedure typically used with mortars or howitzers.

“It is a fact already that the tanks are used because there is not enough artillery,” said the artillery unit commander, who asked to go by his nom de guerre, Razor. His unit of 122-millimeter, self-propelled howitzers had run out of Ukrainian ammunition and was now using Czech-supplied shells.

But ammunition can be fickle. Decades-old ammunition can become unreliable if not stored properly over time, potentially leading to more duds. Another soldier, who spoke on the condition of anonymity, said that a batch of Czech-supplied rockets were faulty, with only three out of 40 firing.

Ukrainian soldiers wounded in combat have also voiced dismay about the paltry artillery support, which they blamed on a lack of ammunition.

“There is not an hour with a pause” in Russian bombardments, Lt. Oleksandr Kolesnikov, who was wounded late last month, said in an interview in an ambulance while being evacuated to a hospital to the west. “The artillery is very intense.” He said his commander called in artillery in response but received only one salvo.

The Russian artillery superiority has frightened soldiers, he said. “In war, everything is scary and we fear everything. Only idiots are not afraid.”

Reporting was contributed by Oleksandr Chubko from Kramatorsk, Ukraine, Maria Varenikova from Barvinkove, Ukraine, Matina Stevis-Gridneff from Brussels and Helene Cooper and John Ismay from Washington.