WASHINGTON — When Russia seized Crimea in 2014, President Vladimir V. Putin was so worried about Russian casualty figures coming to light that authorities accosted journalists who tried to cover funerals of some of the 400 troops killed during that one-month campaign.
But Moscow may be losing that many soldiers daily in Mr. Putin’s latest invasion of Ukraine, American and European officials said. The mounting toll for Russian troops exposes a potential weakness for the Russian president at a time when he is still claiming, publicly, that he is engaged only in a limited military operation in Ukraine’s separatist east.
No one can say with certainty just how many Russian troops have died since last Thursday, when they began what is turning into a long march to Kyiv, the capital. Some Russian units have put down their arms and refused to fight, the Pentagon said Tuesday. Major Ukrainian cities have withstood the onslaught thus far.
American officials had expected the northeastern city of Kharkiv to fall in a day, for example, but Ukrainian troops there have fought back and regained control despite furious rocket fire. The bodies of Russian soldiers have been left in areas surrounding Kharkiv. Videos and photos on social media show charred remains of tanks and armored vehicles, their crews dead or wounded.
The Russian Defense Ministry spokesman, Maj. Gen. Igor Konashenkov, acknowledged on Sunday for the first time that “there are dead and wounded” Russian troops but offered no numbers. He insisted Ukrainian losses were “many times” higher. Ukraine has said its forces have killed more than 5,300 Russian troops.
Neither side’s claims have been independently verified, and Biden administration officials have refused to discuss casualty figures publicly. But one American official put the Russian losses as of Monday at 2,000, an estimate with which two European officials concurred.
Senior Pentagon officials told lawmakers in closed briefings on Monday that Russian and Ukrainian military deaths appeared to be the same, at around 1,500 on each side in the first five days, congressional officials said. But they cautioned that the figures — based on satellite imagery, communication intercepts, social media and on-the-ground media reports — were estimates.
For a comparison, nearly 2,500 American troops were killed in Afghanistan over 20 years of war.
For Mr. Putin, the rising death toll could damage any remaining domestic support for his Ukrainian endeavors. Russian memories are long — and mothers of soldiers, in particular, American officials say, could easily hark back to the 15,000 troops killed when the Soviet Union invaded and occupied Afghanistan, or the thousands killed in Chechnya.
Russia has deployed field hospitals near the front lines, say military analysts, who have also monitored ambulances driving back and forth from Russian units to hospitals in neighboring Belarus, Moscow’s ally.
“Given the many reports of over 4,000 Russians killed in action, it is clear that something dramatic is happening,” said Adm. James G. Stavridis, who was NATO’s supreme allied commander before his retirement. “If Russian losses are this significant, Vladimir Putin is going to have some difficult explaining to do on his home front.”
Representative Adam B. Schiff, Democrat of California and the chairman of the House Intelligence Committee, added, “There are going to be a lot of Russians going home in body bags and a lot of Russian families grieving the longer this goes on.”
In particular, Pentagon officials and military analysts said it was surprising that Russian soldiers had left behind the bodies of their comrades.
“It’s been shocking to see that they’re leaving their fallen brethren behind on the battlefield,” said Evelyn Farkas, the top Pentagon official for Russia and Ukraine during the Obama administration. “Eventually the moms will be like, ‘Where’s Yuri? Where’s Maksim?’”
Already, the Ukrainian government has begun answering that question. On Sunday, authorities launched a website that they said was meant to help Russian families track down information about soldiers who may have been killed or captured. The site, which states it was created by Ukraine’s Ministry of Internal Affairs, says it is providing videos of captured Russian soldiers, some of them injured. The pictures and videos change throughout the day.
“If your relatives or friends are in Ukraine and participate in the war against our people — here you can get information about their fate,” the site says.
The name of the site, www.200rf.com, is a grim reference to Cargo 200, a military code word that was used by the Soviet Union to refer to the bodies of soldiers put in zinc-lined coffins for transport away from the battlefield; it is a euphemism for troops killed in war.
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The website is part of a campaign launched by Ukraine and the West to counter what American officials characterize as Russian disinformation, which includes Russia’s insistence before the invasion that the troops surrounding Ukraine were simply there for military exercises. Information and the battle for public opinion around the world have come to play an outsize part in a war that has come to seem like a David vs. Goliath contest.
On Monday, Ukraine’s ambassador to the United Nations, Sergiy Kyslytsya, read out before the General Assembly what he said were the final text messages from a Russian soldier to his mother. They were obtained, he said, by Ukrainian forces after the soldier was killed. “We were told that they would welcome us and they are falling under our armored vehicles, throwing themselves under the wheels and not allowing us to pass,” he wrote, according to Mr. Kyslytsya. “They call us fascists. Mama, this is so hard.”
The decision to read those texts, Russia experts and Pentagon officials said, was a not-so-veiled reminder to Mr. Putin of the role Russian mothers have had in bringing attention to military losses that the government tried to keep secret. In fact, a group now called the Union of Committees of Soldiers’ Mothers of Russia played a pivotal part in opening up the military to public scrutiny and in influencing perceptions of military service, Julie Elkner, a Russia historian, wrote in The Journal of Power Institutions in Post-Soviet Societies.
On Tuesday, a senior Pentagon official said entire Russian units have laid down their arms without a fight after confronting surprisingly stiff Ukrainian defense. In some cases, Russian troops have punched holes in their vehicles’ gas tanks, presumably to avoid combat, the official said.
The Pentagon official, who spoke on the condition of anonymity to discuss the operational developments, declined to say how the military had made these assessments — presumably from a mosaic of intelligence including statements from captured Russian soldiers and communications intercepts — or how widespread these setbacks might be across the sprawling battlefield.
Images of body bags or coffins, or soldiers killed and left on the battlefield, a Biden administration official said, would prove the most damaging to Mr. Putin at home.
Ukrainian officials are using the reports and images on social media of Russian casualties to try to undercut the morale of the invading Russian forces.
On Monday, Ukraine’s defense minister, Oleksiy Reznikov, offered Russian soldiers cash and amnesty if they surrendered.
“Russian soldier! You were brought to our land to kill and die,” he said. “Do not follow criminal orders. We guarantee you a full amnesty and 5 million rubles if you lay down your arms. For those who continue to behave like an occupier, there will be no mercy.”
Thomas Gibbons-Neff and Catie Edmondson contributed reporting. Kitty Bennett contributed research.
